 6.6.4.1: How much work is done in lifting a 40kg sandbag to a height 9. of ...
 6.6.5.1: Find the average value of the function on the given interval.
 6.6.1.1: Find the area of the shaded region.
 6.6.2.1: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.1: Let be the solid obtained by rotating the region shown in the figur...
 6.6.4.2: Find the work done if a constant force of 100 lb is used to pull a ...
 6.6.5.2: Find the average value of the function on the given interval.
 6.6.1.2: Find the area of the shaded region.
 6.6.2.2: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.2: Let be the solid obtained by rotating the region shown in the figur...
 6.6.4.3: A particle is moved along the xaxis by a force that measures 101 x...
 6.6.5.3: Find the average value of the function on the given interval.
 6.6.1.3: Find the area of the shaded region.
 6.6.2.3: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.3: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.4: When a particle is located a distance meters from the origin, a for...
 6.6.5.4: Find the average value of the function on the given interval.
 6.6.1.4: Find the area of the shaded region.
 6.6.2.4: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.4: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.5: Shown is the graph of a force function (in newtons) that increases ...
 6.6.5.5: Find the average value of the function on the given interval.
 6.6.1.5: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.5: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.5: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.6: The table shows values of a force function , where is measured in m...
 6.6.5.6: Find the average value of the function on the given interval.
 6.6.1.6: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.6: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.6: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.7: A force of 10 lb is required to hold a spring stretched 4 in. beyon...
 6.6.5.7: Find the average value of the function on the given interval.
 6.6.1.7: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.7: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.7: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.8: A spring has a natural length of 20 cm. If a 25N force is required...
 6.6.5.8: Find the average value of the function on the given interval.
 6.6.1.8: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.8: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.8: Let be the volume of the solid obtained by rotating about the axis...
 6.6.4.9: Suppose that 2 J of work is needed to stretch a spring from its nat...
 6.6.5.9: (a) Find the average value of on the given interval. (b) Find such ...
 6.6.1.9: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.9: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.9: Use the method of cylindrical shells to find the volume of the soli...
 6.6.4.10: If the work required to stretch a spring 1 ft beyond its natural le...
 6.6.5.10: (a) Find the average value of on the given interval. (b) Find such ...
 6.6.1.10: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.10: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.10: Use the method of cylindrical shells to find the volume of the soli...
 6.6.4.11: A spring has natural length 20 cm. Compare the work done in stretch...
 6.6.5.11: (a) Find the average value of on the given interval. (b) Find such ...
 6.6.1.11: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.11: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.11: Use the method of cylindrical shells to find the volume of the soli...
 6.6.4.12: If 6 J of work is needed to stretch a spring from 10 cm to 12 cm an...
 6.6.5.12: (a) Find the average value of on the given interval. (b) Find such ...
 6.6.1.12: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.12: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.12: Use the method of cylindrical shells to find the volume of the soli...
 6.6.4.13: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.13: If is continuous and , show that takes on the value 4 at least once...
 6.6.1.13: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.13: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.13: Use the method of cylindrical shells to find the volume of the soli...
 6.6.4.14: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.14: Find the numbers such that the average value of f x 2 6x 3x 0, b 2b...
 6.6.1.14: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.14: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.14: Use the method of cylindrical shells to find the volume of the soli...
 6.6.3.15: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.15: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.15: The table gives values of a continuous function. Use the Midpoint R...
 6.6.1.15: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.15: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.16: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.16: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.16: The velocity graph of an accelerating car is shown. (a) Estimate th...
 6.6.1.16: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.16: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.17: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.17: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.17: In a certain city the temperature (in F) hours after 9 AM was model...
 6.6.1.17: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.17: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.18: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.18: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.18: (a) A cup of coffee has temperature 95 C and takes 30 minutes to co...
 6.6.1.18: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.18: Find the volume of the solid obtained by rotating the region 2 boun...
 6.6.3.19: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.19: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.19: The linear density in a rod 8 m long is , where is measured in mete...
 6.6.1.19: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.19: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.20: Use the method of cylindrical shells to find the volume generated b...
 6.6.4.20: Show how to approximate the required work by a Riemann sum. Then ex...
 6.6.5.20: If a freely falling body starts from rest, then its displacement is...
 6.6.1.20: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.20: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.21: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.4.21: A tank is full of water. Find the work required to pump the water o...
 6.6.5.21: Use the result of Exercise 79 in Section 5.5 to compute the average...
 6.6.1.21: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.21: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.22: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.4.22: A tank is full of water. Find the work required to pump the water o...
 6.6.5.22: The velocity of blood that flows in a blood vessel with radius and ...
 6.6.1.22: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.22: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.23: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.4.23: A tank is full of water. Find the work required to pump the water o...
 6.6.5.23: Prove the Mean Value Theorem for Integrals by applying the Mean Val...
 6.6.1.23: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.23: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.24: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.4.24: A tank is full of water. Find the work required to pump the water o...
 6.6.5.24: If fave a, b denotes the average value of on the interval and , sho...
 6.6.1.24: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.24: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.25: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.4.25: Suppose that for the tank in Exercise 21 the pump breaks down after...
 6.6.1.25: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.25: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.26: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.4.26: Solve Exercise 22 if the tank is half full of oil that has a densit...
 6.6.1.26: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.26: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.27: Use the Midpoint Rule with to estimate the volume obtained by rotat...
 6.6.4.27: When gas expands in a cylinder with radius , the pressure at any gi...
 6.6.1.27: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.27: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.28: If the region shown in the figure is rotated about the axis to for...
 6.6.4.28: In a steam engine the pressure and volume of steam satisfy the equa...
 6.6.1.28: Sketch the region enclosed by the given curves. Decide whether to i...
 6.6.2.28: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.29: Each integral represents the volume of a solid. Describe the solid.
 6.6.4.29: Newtons Law of Gravitation states that two bodies with masses and a...
 6.6.1.29: Use calculus to find the area of the triangle with the given vertices.
 6.6.2.29: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.30: Each integral represents the volume of a solid. Describe the solid.
 6.6.4.30: Use Newtons Law of Gravitation to compute the work required to laun...
 6.6.1.30: Use calculus to find the area of the triangle with the given vertices.
 6.6.2.30: Refer to the figure and find the volume generated by rotating the g...
 6.6.3.31: Each integral represents the volume of a solid. Describe the solid.
 6.6.1.31: Evaluate the integral and interpret it as the area of a region. Ske...
 6.6.2.31: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.3.32: Each integral represents the volume of a solid. Describe the solid.
 6.6.1.32: Evaluate the integral and interpret it as the area of a region. Ske...
 6.6.2.32: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.3.33: Use a graph to estimate the coordinates of the points of intersect...
 6.6.1.33: Use the Midpoint Rule with to approximate the area of the region bo...
 6.6.2.33: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.3.34: Use a graph to estimate the coordinates of the points of intersect...
 6.6.1.34: Use the Midpoint Rule with to approximate the area of the region bo...
 6.6.2.34: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.3.35: Use a computer algebra system to find the exact volume of the solid...
 6.6.1.35: Use a graph to find approximate coordinates of the points of inter...
 6.6.2.35: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.3.36: Use a computer algebra system to find the exact volume of the solid...
 6.6.1.36: Use a graph to find approximate coordinates of the points of inter...
 6.6.2.36: Set up, but do not evaluate, an integral for the volume of the soli...
 6.6.3.37: The region bounded by the given curves is rotated about the specifi...
 6.6.1.37: Use a graph to find approximate coordinates of the points of inter...
 6.6.2.37: Use a graph to find approximate coordinates of the points of inter...
 6.6.3.38: The region bounded by the given curves is rotated about the specifi...
 6.6.1.38: Use a graph to find approximate coordinates of the points of inter...
 6.6.2.38: Use a graph to find approximate coordinates of the points of inter...
 6.6.3.39: The region bounded by the given curves is rotated about the specifi...
 6.6.1.39: Use a computer algebra system to find the exact area enclosed by th...
 6.6.2.39: Use a computer algebra system to find the exact volume of the solid...
 6.6.3.40: The region bounded by the given curves is rotated about the specifi...
 6.6.1.40: Sketch the region in the plane defined by the inequalities x 2y 0 ...
 6.6.2.40: Use a computer algebra system to find the exact volume of the solid...
 6.6.3.41: The region bounded by the given curves is rotated about the specifi...
 6.6.1.41: Racing cars driven by Chris and Kelly are side by side at the start...
 6.6.2.41: Each integral represents the volume of a solid. Describe the solid....
 6.6.3.42: The region bounded by the given curves is rotated about the specifi...
 6.6.1.42: The widths (in meters) of a kidneyshaped swimming pool were measur...
 6.6.2.42: Each integral represents the volume of a solid. Describe the solid....
 6.6.3.43: Use cylindrical shells to find the volume of the solid.
 6.6.1.43: A crosssection of an airplane wing is shown. Measurements of the h...
 6.6.2.43: Each integral represents the volume of a solid. Describe the solid....
 6.6.3.44: Use cylindrical shells to find the volume of the solid.
 6.6.1.44: If the birth rate of a population is people per year and the death ...
 6.6.2.44: Each integral represents the volume of a solid. Describe the solid....
 6.6.3.45: Use cylindrical shells to find the volume of the solid.
 6.6.1.45: Two cars, A and B, start side by side and accelerate from rest. The...
 6.6.2.45: A CAT scan produces equally spaced crosssectional views of a human...
 6.6.3.46: Suppose you make napkin rings by drilling holes with different diam...
 6.6.1.46: The figure shows graphs of the marginal revenue function and the ma...
 6.6.2.46: A log 10 m long is cut at 1meter intervals and its crosssectional ...
 6.6.1.47: The curve with equation is called Tschirnhausens cubic. If you grap...
 6.6.2.47: (a) If the region shown in the figure is rotated about the axis to...
 6.6.1.48: Find the area of the region bounded by the parabola , the tangent l...
 6.6.2.48: (a) A model for the shape of a birds egg is obtained by rotating ab...
 6.6.1.49: Find the number such that the line divides the region bounded by th...
 6.6.2.49: Find the volume of the described solid . A right circular cone with...
 6.6.1.50: (a) Find the number such that the line bisects the area under the c...
 6.6.2.50: Find the volume of the described solid . A frustum of a right circu...
 6.6.1.51: Find the values of such that the area of the region bounded by the ...
 6.6.2.51: Find the volume of the described solid . A cap of a sphere with rad...
 6.6.1.52: Suppose that 0 c 2 . For what value of is the area of the region en...
 6.6.2.52: Find the volume of the described solid . A frustum of a pyramid wit...
 6.6.1.53: For what values of do the line and the curve y x x enclose a region...
 6.6.2.53: Find the volume of the described solid . A pyramid with height and ...
 6.6.2.54: Find the volume of the described solid . A pyramid with height and ...
 6.6.2.55: Find the volume of the described solid . A tetrahedron with three m...
 6.6.2.56: Find the volume of the described solid . The base of is a circular ...
 6.6.2.57: Find the volume of the described solid . The base of is an elliptic...
 6.6.2.58: Find the volume of the described solid . The base of is the triangu...
 6.6.2.59: Find the volume of the described solid . The base of is the same ba...
 6.6.2.60: Find the volume of the described solid . The base of is the region ...
 6.6.2.61: Find the volume of the described solid . The base of is the same ba...
 6.6.2.62: The base of is a circular disk with radius . Parallel crosssections...
 6.6.2.63: (a) Set up an integral for the volume of a solid torus (the donuts...
 6.6.2.64: Solve Example 9 taking crosssections to be parallel to the line of...
 6.6.2.65: (a) Cavalieris Principle states that if a family of parallel planes...
 6.6.2.66: Find the volume common to two circular cylinders, each with radius ...
 6.6.2.67: Find the volume common to two spheres, each with radius , if the ce...
 6.6.2.68: A bowl is shaped like a hemisphere with diameter 30 cm. A ball with...
 6.6.2.69: A hole of radius is bored through a cylinder of radius at right ang...
 6.6.2.70: A hole of radius is bored through the center of a sphere of radius ...
 6.6.2.71: Some of the pioneers of calculus, such as Kepler and Newton, were i...
 6.6.2.72: Suppose that a region has area and lies above the axis. When is ro...
Solutions for Chapter 6: Applications of Integration
Full solutions for Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign)  6th Edition
ISBN: 9780495011699
Solutions for Chapter 6: Applications of Integration
Get Full SolutionsChapter 6: Applications of Integration includes 225 full stepbystep solutions. Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780495011699. Since 225 problems in chapter 6: Applications of Integration have been answered, more than 87273 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign), edition: 6. This expansive textbook survival guide covers the following chapters and their solutions.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Dependent event
An event whose probability depends on another event already occurring

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Extracting square roots
A method for solving equations in the form x 2 = k.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Instantaneous rate of change
See Derivative at x = a.

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Range (in statistics)
The difference between the greatest and least values in a data set.

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Time plot
A line graph in which time is measured on the horizontal axis.

xzplane
The points x, 0, z in Cartesian space.