 6.6.1: Find the area of the region bounded above by , bounded below by , a...
 6.6.2: Find the area of the region enclosed by the parabolas y=x2 and y 2x...
 6.6.3: Find the approximate area of the region bounded by the curves and
 6.6.4: Figure 8 shows velocity curves for two cars, A and B, that start si...
 6.6.5: Find the area of the region bounded by the curves , , , andx 2
 6.6.6: Find the area enclosed by the line and the parabola y 2 2x 6
 6.6.7: Find the area of the shaded region
 6.6.8: Find the area of the shaded region
 6.6.9: Find the area of the shaded region
 6.6.10: Find the area of the shaded region
 6.6.11: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.12: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.13: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.14: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.15: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.16: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.17: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.18: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.19: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.20: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.21: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.22: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.23: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.24: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.25: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.26: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.27: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.28: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.29: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.30: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.31: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.32: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.33: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.34: Sketch the region enclosed by the given curves. Decidewhether to in...
 6.6.35: Use calculus to find the area of the triangle with the givenvertice...
 6.6.36: Use calculus to find the area of the triangle with the givenvertice...
 6.6.37: Evaluate the integral and interpret it as the area of aregion. Sket...
 6.6.38: Evaluate the integral and interpret it as the area of aregion. Sket...
 6.6.39: Use the Midpoint Rule with to approximate thearea of the region bou...
 6.6.40: Use the Midpoint Rule with to approximate thearea of the region bou...
 6.6.41: Use a graph to find approximate coordinates of the pointsof inters...
 6.6.42: Use a graph to find approximate coordinates of the pointsof inters...
 6.6.43: Use a graph to find approximate coordinates of the pointsof inters...
 6.6.44: Use a graph to find approximate coordinates of the pointsof inters...
 6.6.45: Use a computer algebra system to find the exact area enclosed by th...
 6.6.46: Sketch the region in the plane defined by the inequalities , and f...
 6.6.47: Racing cars driven by Chris and Kelly are side by side at the start...
 6.6.48: The widths (in meters) of a kidneyshaped swimming pool were measur...
 6.6.49: A crosssection of an airplane wing is shown. Measurements of the h...
 6.6.50: If the birth rate of a population is people per year and the death ...
 6.6.51: Two cars, A and B, start side by side and accelerate from rest. The...
 6.6.52: The figure shows graphs of the marginal revenue function and the ma...
 6.6.53: The curve with equation is called Tschirnhausens cubic. If you grap...
 6.6.54: Find the area of the region bounded by the parabola , the tangent l...
 6.6.55: Find the number such that the line divides the region bounded by th...
 6.6.56: a) Find the number such that the line bisects the area under the cu...
 6.6.57: Find the values of such that the area of the region bounded by the ...
 6.6.58: Suppose that . For what value of is the area of the region enclosed...
 6.6.59: For what values of do the line and the curve y x x enclose a region...
 6.6.60: Show that the volume of a sphere of radius is V 4 3r 3
 6.6.61: Find the volume of the solid obtained by rotating about the xaxis ...
 6.6.62: Find the volume of the solid obtained by rotating the region bounde...
 6.6.63: The region enclosed by the curves and is rotated about the axis. F...
 6.6.64: Find the volume of the solid obtained by rotating the region in Exa...
 6.6.65: Find the volume of the solid obtained by rotating the region in Exa...
 6.6.66: Find the volume of the solid obtained by rotating the region in Exa...
 6.6.67: Find the volume of a pyramid whose base is a square with side and w...
 6.6.68: A wedge is cut out of a circular cylinder of radius 4 by two planes...
 6.6.69: A wedge is cut out of a circular cylinder of radius 4 by two planes...
 6.6.70: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.71: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.72: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.73: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.74: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.75: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.76: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.77: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.78: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.79: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.80: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.81: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.82: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.83: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.84: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.85: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.86: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.87: Find the volume of the solid obtained by rotating the region 2bound...
 6.6.88: Refer to the figure and find the volume generated by rotating the g...
 6.6.89: Refer to the figure and find the volume generated by rotating the g...
 6.6.90: Refer to the figure and find the volume generated by rotating the g...
 6.6.91: Refer to the figure and find the volume generated by rotating the g...
 6.6.92: Refer to the figure and find the volume generated by rotating the g...
 6.6.93: Refer to the figure and find the volume generated by rotating the g...
 6.6.94: Refer to the figure and find the volume generated by rotating the g...
 6.6.95: Refer to the figure and find the volume generated by rotating the g...
 6.6.96: Refer to the figure and find the volume generated by rotating the g...
 6.6.97: Refer to the figure and find the volume generated by rotating the g...
 6.6.98: Refer to the figure and find the volume generated by rotating the g...
 6.6.99: Refer to the figure and find the volume generated by rotating the g...
 6.6.100: Set up, but do not evaluate, an integral for the volume ofthe solid...
 6.6.101: Set up, but do not evaluate, an integral for the volume ofthe solid...
 6.6.102: Set up, but do not evaluate, an integral for the volume ofthe solid...
 6.6.103: Set up, but do not evaluate, an integral for the volume ofthe solid...
 6.6.104: Set up, but do not evaluate, an integral for the volume ofthe solid...
 6.6.105: Set up, but do not evaluate, an integral for the volume ofthe solid...
 6.6.106: Use a graph to find approximate coordinates of thepoints of inters...
 6.6.107: Use a graph to find approximate coordinates of thepoints of inters...
 6.6.108: Use a computer algebra system to find the exact volumeof the solid ...
 6.6.109: Use a computer algebra system to find the exact volumeof the solid ...
 6.6.110: Each integral represents the volume of a solid. Describethe solidy ...
 6.6.111: Each integral represents the volume of a solid. Describethe solidy ...
 6.6.112: Each integral represents the volume of a solid. Describethe solidy ...
 6.6.113: Each integral represents the volume of a solid. Describethe solid y...
 6.6.114: A CAT scan produces equally spaced crosssectional views of a human...
 6.6.115: A log 10 m long is cut at 1meter intervals and its crosssectional ...
 6.6.116: (a) If the region shown in the figure is rotated about the axis to...
 6.6.117: a) A model for the shape of a birds egg is obtained by rotating abo...
 6.6.118: A right circular cone with height and base radius r
 6.6.119: Find the volume of the described solid s A frustum of a right circu...
 6.6.120: Find the volume of the described solid s A cap of a sphere with rad...
 6.6.121: Find the volume of the described solid s A frustum of a pyramid wit...
 6.6.122: Find the volume of the described solid s A pyramid with height and ...
 6.6.123: Find the volume of the described solid s A pyramid with height and ...
 6.6.124: Find the volume of the described solid s A tetrahedron with three m...
 6.6.125: Find the volume of the described solid s The base of is a circular ...
 6.6.126: Find the volume of the described solid s The base of is an elliptic...
 6.6.127: Find the volume of the described solid s The base of is the triangu...
 6.6.128: Find the volume of the described solid s The base of is the same ba...
 6.6.129: Find the volume of the described solid s The base of is the region ...
 6.6.130: Find the volume of the described solid s The base of is the same ba...
 6.6.131: The base of is a circular disk with radius . Parallel crosssections...
 6.6.132: (a) Set up an integral for the volume of a solid torus (the donuts...
 6.6.133: a) Cavalieris Principle states that if a family of parallel planes ...
 6.6.134: Find the volume common to two circular cylinders, each with radius ...
 6.6.135: Find the volume common to two spheres, each with radius , if the ce...
 6.6.136: A bowl is shaped like a hemisphere with diameter 30 cm. A ball with...
 6.6.137: A hole of radius is bored through a cylinder of radius at right ang...
 6.6.138: Suppose that a region has area and lies above the axis. When is ro...
 6.6.139: Find the volume of the solid obtained by rotating about the axis t...
 6.6.140: Find the volume of the solid obtained by rotating about the axis t...
 6.6.141: Use cylindrical shells to find the volume of the solid obtained by ...
 6.6.142: Find the volume of the solid obtained by rotating the region bounde...
 6.6.143: Let be the solid obtained by rotating the region shown in the figur...
 6.6.144: Let be the solid obtained by rotating the region shown in the figur...
 6.6.145: Use the method of cylindrical shells to find the volume generatedby...
 6.6.146: Use the method of cylindrical shells to find the volume generatedby...
 6.6.147: Use the method of cylindrical shells to find the volume generatedby...
 6.6.148: Use the method of cylindrical shells to find the volume generatedby...
 6.6.149: Use the method of cylindrical shells to find the volume generatedby...
 6.6.150: Let be the volume of the solid obtained by rotating about the axis...
 6.6.151: Use the method of cylindrical shells to find the volume of thesolid...
 6.6.152: Use the method of cylindrical shells to find the volume of thesolid...
 6.6.153: Use the method of cylindrical shells to find the volume of thesolid...
 6.6.154: Use the method of cylindrical shells to find the volume of thesolid...
 6.6.155: Use the method of cylindrical shells to find the volume of thesolid...
 6.6.156: Use the method of cylindrical shells to find the volume of thesolid...
 6.6.157: Use the method of cylindrical shells to find the volume generated b...
 6.6.158: Use the method of cylindrical shells to find the volume generated b...
 6.6.159: Use the method of cylindrical shells to find the volume generated b...
 6.6.160: Use the method of cylindrical shells to find the volume generated b...
 6.6.161: Use the method of cylindrical shells to find the volume generated b...
 6.6.162: Use the method of cylindrical shells to find the volume generated b...
 6.6.163: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.164: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.165: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.166: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.167: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.168: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.169: Use the Midpoint Rule with to estimate the volume obtained by rotat...
 6.6.170: If the region shown in the figure is rotated about the axis to for...
 6.6.171: Each integral represents the volume of a solid. Describethe solidy ...
 6.6.172: Each integral represents the volume of a solid. Describethe solid2y...
 6.6.173: Each integral represents the volume of a solid. Describethe solidy ...
 6.6.174: Each integral represents the volume of a solid. Describethe solidy ...
 6.6.175: Use a graph to estimate the coordinates of the points ofintersecti...
 6.6.176: Use a graph to estimate the coordinates of the points ofintersecti...
 6.6.177: Use a computer algebra system to find the exact volume of the solid...
 6.6.178: Use a computer algebra system to find the exact volume of the solid...
 6.6.179: The region bounded by the given curves is rotated about the specifi...
 6.6.180: The region bounded by the given curves is rotated about the specifi...
 6.6.181: The region bounded by the given curves is rotated about the specifi...
 6.6.182: The region bounded by the given curves is rotated about the specifi...
 6.6.183: The region bounded by the given curves is rotated about the specifi...
 6.6.184: The region bounded by the given curves is rotated about the specifi...
 6.6.185: Use cylindrical shells to find the volume of the solid. A sphere of...
 6.6.186: Use cylindrical shells to find the volume of the solid. The solid t...
 6.6.187: Use cylindrical shells to find the volume of the solid. A right cir...
 6.6.188: Suppose you make napkin rings by drilling holes with different diam...
 6.6.189: a) How much work is done in lifting a 1.2kg book off the floor to ...
 6.6.190: When a particle is located a distance feet from the origin, a force...
 6.6.191: A force of 40 N is required to hold a spring that has been stretche...
 6.6.192: A 200lb cable is 100 ft long and hangs vertically from the top of ...
 6.6.193: A tank has the shape of an inverted circular cone with height 10 m ...
 6.6.194: How much work is done in lifting a 40kg sandbag to a height 9. of ...
 6.6.195: Find the work done if a constant force of 100 lb is used to pull a ...
 6.6.196: A particle is moved along the axis by a force that measures pounds...
 6.6.197: When a particle is located a distance meters from the origin, a for...
 6.6.198: Shown is the graph of a force function (in newtons) that increases ...
 6.6.199: The table shows values of a force function , where is measured in m...
 6.6.200: A force of 10 lb is required to hold a spring stretched 4 in. beyon...
 6.6.201: A spring has a natural length of 20 cm. If a 25N force is required...
 6.6.202: Suppose that 2 J of work is needed to stretch a spring from its nat...
 6.6.203: If the work required to stretch a spring 1 ft beyond its natural le...
 6.6.204: A spring has natural length 20 cm. Compare the work done in stretch...
 6.6.205: If 6 J of work is needed to stretch a spring from 10 cm to 12 cm an...
 6.6.206: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.207: A heavy rope, 50 ft long, weighs and hangs over the edge of a build...
 6.6.208: A chain lying on the ground is 10 m long and its mass is 80 kg. How...
 6.6.209: A cable that weighs is used to lift 800 lb of coal up a mine shaft ...
 6.6.210: A bucket that weighs 4 lb and a rope of negligible weight are used ...
 6.6.211: A leaky 10kg bucket is lifted from the ground to a height of 12 m ...
 6.6.212: A 10ft chain weighs 25 lb and hangs from a ceiling. Find the work ...
 6.6.213: An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find...
 6.6.214: A circular swimming pool has a diameter of 24 ft, the sides are 5 f...
 6.6.215: A tank is full of water. Find the work required to pump the water o...
 6.6.216: A tank is full of water. Find the work required to pump the water o...
 6.6.217: A tank is full of water. Find the work required to pump the water o...
 6.6.218: A tank is full of water. Find the work required to pump the water o...
 6.6.219: Suppose that for the tank in Exercise 21 the pump breaks down after...
 6.6.220: Solve Exercise 22 if the tank is half full of oil that has a densit...
 6.6.221: When gas expands in a cylinder with radius , the pressure at any gi...
 6.6.222: In a steam engine the pressure and volume of steam satisfy the equa...
 6.6.223: Newtons Law of Gravitation states that two bodies with masses and a...
 6.6.224: Use Newtons Law of Gravitation to compute the work required to laun...
 6.6.225: Find the average value of the function on the interval .
 6.6.226: Find the average value of the function on the given interval
 6.6.227: Find the average value of the function on the given interval
 6.6.228: Find the average value of the function on the given interval
 6.6.229: Find the average value of the function on the given interval txs , ...
 6.6.230: Find the average value of the function on the given interval f ttet...
 6.6.231: Find the average value of the function on the given interval fsec22...
 6.6.232: Find the average value of the function on the given interval hxcos4...
 6.6.233: Find the average value of the function on the given interval hu3 2u...
 6.6.234: a) Find the average value of on the given interval.(b) Find such th...
 6.6.235: a) Find the average value of on the given interval.(b) Find such th...
 6.6.236: a) Find the average value of on the given interval.(b) Find such th...
 6.6.237: a) Find the average value of on the given interval.(b) Find such th...
 6.6.238: If is continuous and , show that takes on the value 4 at least once...
 6.6.239: Find the numbers such that the average value of on the interval is ...
 6.6.240: The velocity graph of an accelerating car is shown. (a) Estimate th...
 6.6.241: In a certain city the temperature (in F) hours after 9 AM was model...
 6.6.242: a) A cup of coffee has temperature 95 C and takes 30 minutes to coo...
 6.6.243: The linear density in a rod 8 m long is , where is measured in mete...
 6.6.244: If a freely falling body starts from rest, then its displacement is...
 6.6.245: Use the result of Exercise 79 in Section 5.5 to compute the average...
 6.6.246: The velocity of blood that flows in a blood vessel with radius and ...
 6.6.247: Prove the Mean Value Theorem for Integrals by applying the Mean Val...
 6.6.248: If denotes the average value of on the interval and , show that fav...
 6.6.249: Draw two typical curves and , where S for . Show how to approximate...
 6.6.250: Suppose that Sue runs faster than Kathy throughout a 1500meter rac...
 6.6.251: (a) Suppose is a solid with known crosssectional areas. Explain ho...
 6.6.252: (a) What is the volume of a cylindrical shell? (b) Explain how to u...
 6.6.253: Suppose that you push a book across a 6meterlong table by exertin...
 6.6.254: (a) What is the average value of a function on an interval ? (b) Wh...
 6.6.255: Find the area of the region bounded by the given curves.x 2 , y 4x ...
 6.6.256: Find the area of the region bounded by the given curves.y 1x, y x 2...
 6.6.257: Find the area of the region bounded by the given curves.y 1x, y x 2...
 6.6.258: Find the area of the region bounded by the given curves.y 1x, y x 2...
 6.6.259: Find the area of the region bounded by the given curves.y 1x, y x 2...
 6.6.260: Find the area of the region bounded by the given curves.y 1x, y x 2...
 6.6.261: Find the volume of the solid obtained by rotating the region bounde...
 6.6.262: Find the volume of the solid obtained by rotating the region bounde...
 6.6.263: Find the volume of the solid obtained by rotating the region bounde...
 6.6.264: Find the volume of the solid obtained by rotating the region bounde...
 6.6.265: Find the volume of the solid obtained by rotating the region bounde...
 6.6.266: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.267: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.268: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.269: Find the volumes of the solids obtained by rotating the region boun...
 6.6.270: Let be the region in the first quadrant bounded by the curves and ....
 6.6.271: Let be the region bounded by the curves , and . Use the Midpoint Ru...
 6.6.272: Let be the region bounded by the curves and . Estimate the followin...
 6.6.273: Each integral represents the volume of a solid. Describethe solid2 ...
 6.6.274: Each integral represents the volume of a solid. Describethe solid2 ...
 6.6.275: Each integral represents the volume of a solid. Describethe solid0 ...
 6.6.276: Each integral represents the volume of a solid. Describethe solid4 ...
 6.6.277: The base of a solid is a circular disk with radius 3. Find the volu...
 6.6.278: The base of a solid is the region bounded by the parabolas and . Fi...
 6.6.279: The height of a monument is 20 m. A horizontal crosssection at a d...
 6.6.280: a) The base of a solid is a square with vertices located at , and ....
 6.6.281: A force of 30 N is required to maintain a spring stretched from its...
 6.6.282: A 1600lb elevator is suspended by a 200ft cable that weighs 10 lb...
 6.6.283: A tank full of water has the shape of a paraboloid of revolution as...
 6.6.284: Find the average value of the function on the interval
 6.6.285: If is a continuous function, what is the limit as of the average va...
 6.6.286: Let be the region bounded by , , and , where . Let be the region bo...
 6.6.287: a) Find a positive continuous function such that the area under the...
 6.6.288: There is a line through the origin that divides the region bounded ...
 6.6.289: The figure shows a horizontal line intersecting the curve . Find th...
 6.6.290: A cylindrical glass of radius and height is filled with water and t...
 6.6.291: (a) Show that the volume of a segment of height of a sphere of radi...
 6.6.292: Water in an open bowl evaporates at a rate proportional to the area...
 6.6.293: A sphere of radius 1 overlaps a smaller sphere of radius in such a ...
 6.6.294: The figure shows a curve with the property that, for every point on...
 6.6.295: A paper drinking cup filled with water has the shape of a cone with...
 6.6.296: A clepsydra, or water clock, is a glass container with a small hole...
 6.6.297: A cylindrical container of radius and height is partially filled wi...
 6.6.298: Suppose the graph of a cubic polynomial intersects the parabola whe...
 6.6.299: Suppose we are planning to make a taco from a round tortilla with d...
 6.6.300: If the tangent at a point on the curve intersects the curve again a...
Solutions for Chapter 6: APPLICATIONS OF INTEGRATION
Full solutions for Calculus: Early Transcendentals  6th Edition
ISBN: 9780495011668
Solutions for Chapter 6: APPLICATIONS OF INTEGRATION
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 300 problems in chapter 6: APPLICATIONS OF INTEGRATION have been answered, more than 35514 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780495011668. Chapter 6: APPLICATIONS OF INTEGRATION includes 300 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 6.

Anchor
See Mathematical induction.

Arccosecant function
See Inverse cosecant function.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

Future value of an annuity
The net amount of money returned from an annuity.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Line of travel
The path along which an object travels

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Real zeros
Zeros of a function that are real numbers.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Slope
Ratio change in y/change in x

Square matrix
A matrix whose number of rows equals the number of columns.

Ymax
The yvalue of the top of the viewing window.