 4.1: In Exercises 1 and 2, use the graph of to sketch a graph of To prin...
 4.2: In Exercises 1 and 2, use the graph of to sketch a graph of To prin...
 4.3: In Exercises 3 8, find the indefinite integral.4x dx 2 x 3 dx
 4.4: In Exercises 3 8, find the indefinite integral.
 4.5: In Exercises 3 8, find the indefinite integral.
 4.6: In Exercises 3 8, find the indefinite integral.
 4.7: In Exercises 3 8, find the indefinite integral.
 4.8: In Exercises 3 8, find the indefinite integral.
 4.9: Find the particular solution of the differential equation whose gra...
 4.10: Find the particular solution of the differential equation whose gra...
 4.11: In Exercises 11 and 12, a differential equation, a point, and a slo...
 4.12: In Exercises 11 and 12, a differential equation, a point, and a slo...
 4.13: An airplane taking off from a runway travels 3600 feet before lifti...
 4.14: The speed of a car traveling in a straight line is reduced from 45 ...
 4.15: A ball is thrown vertically upward from ground level with an initia...
 4.16: The table shows the velocities (in miles per hour) of two cars on a...
 4.17: In Exercises 17 and 18, use sigma notation to write the sum.1 31 1 ...
 4.18: In Exercises 17 and 18, use sigma notation to write the sum.3 n 1 1...
 4.19: In Exercises 1922, use the properties of summation and Theorem 4.2 ...
 4.20: In Exercises 1922, use the properties of summation and Theorem 4.2 ...
 4.21: In Exercises 1922, use the properties of summation and Theorem 4.2 ...
 4.22: In Exercises 1922, use the properties of summation and Theorem 4.2 ...
 4.23: Write in sigma notation (a) the sum of the first ten positive odd i...
 4.24: Evaluate each sum for and (a) (b) (c) (d) 5 i2 xi xi1 5 i1 2xi x 2 ...
 4.25: In Exercises 25 and 26, use upper and lower sums to approximate the...
 4.26: In Exercises 25 and 26, use upper and lower sums to approximate the...
 4.27: In Exercises 2730, use the limit process to find the area of the re...
 4.28: In Exercises 2730, use the limit process to find the area of the re...
 4.29: In Exercises 2730, use the limit process to find the area of the re...
 4.30: In Exercises 2730, use the limit process to find the area of the re...
 4.31: Use the limit process to find the area of the region bounded by x 5...
 4.32: Consider the region bounded by and (a) Find the upper and lower sum...
 4.33: In Exercises 33 and 34, write the limit as a definite integral on t...
 4.34: In Exercises 33 and 34, write the limit as a definite integral on t...
 4.35: In Exercises 35 and 36, set up a definite integral that yields the ...
 4.36: In Exercises 35 and 36, set up a definite integral that yields the ...
 4.37: In Exercises 37 and 38, sketch the region whose area is given by th...
 4.38: In Exercises 37 and 38, sketch the region whose area is given by th...
 4.39: Given evaluate (a) (b) (c) (d)
 4.40: Given evaluate (a) (b) (c) (d)
 4.41: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.42: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.43: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.44: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.45: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.46: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.47: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.48: In Exercises 41 48, use the Fundamental Theorem of Calculus to eval...
 4.49: In Exercises 4954, sketch the graph of the region whose area is giv...
 4.50: In Exercises 4954, sketch the graph of the region whose area is giv...
 4.51: In Exercises 4954, sketch the graph of the region whose area is giv...
 4.52: In Exercises 4954, sketch the graph of the region whose area is giv...
 4.53: In Exercises 4954, sketch the graph of the region whose area is giv...
 4.54: In Exercises 4954, sketch the graph of the region whose area is giv...
 4.55: In Exercises 55 and 56, determine the area of the given region
 4.56: In Exercises 55 and 56, determine the area of the given region
 4.57: In Exercises 57 and 58, sketch the region bounded by the graphs of ...
 4.58: In Exercises 57 and 58, sketch the region bounded by the graphs of ...
 4.59: In Exercises 59 and 60, find the average value of the function over...
 4.60: In Exercises 59 and 60, find the average value of the function over...
 4.61: In Exercises 6164, use the Second Fundamental Theorem of Calculus t...
 4.62: In Exercises 6164, use the Second Fundamental Theorem of Calculus t...
 4.63: In Exercises 6164, use the Second Fundamental Theorem of Calculus t...
 4.64: In Exercises 6164, use the Second Fundamental Theorem of Calculus t...
 4.65: In Exercises 6576, find the indefinite integral.3 x dx 23 dx
 4.66: In Exercises 6576, find the indefinite integral.x 1 x 2 3 x dx 2
 4.67: In Exercises 6576, find the indefinite integral.
 4.68: In Exercises 6576, find the indefinite integral.
 4.69: In Exercises 6576, find the indefinite integral.
 4.70: In Exercises 6576, find the indefinite integral.
 4.71: In Exercises 6576, find the indefinite integral.
 4.72: In Exercises 6576, find the indefinite integral.
 4.73: In Exercises 6576, find the indefinite integral.
 4.74: In Exercises 6576, find the indefinite integral.
 4.75: In Exercises 6576, find the indefinite integral.
 4.76: In Exercises 6576, find the indefinite integral.sec 2x tan 2x dx
 4.77: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.78: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.79: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.80: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.81: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.82: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.83: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.84: In Exercises 7784, evaluate the definite integral. Use a graphing u...
 4.85: In Exercises 85 and 86, a differential equation, a point, and a slo...
 4.86: In Exercises 85 and 86, a differential equation, a point, and a slo...
 4.87: In Exercises 87 and 88, find the area of the region. Use a graphing...
 4.88: In Exercises 87 and 88, find the area of the region. Use a graphing...
 4.89: The normal monthly precipitation in Portland, Oregon can be approxi...
 4.90: After exercising for a few minutes, a person has a respiratory cycl...
 4.91: In Exercises 9194, use the Trapezoidal Rule and Simpsons Rule with ...
 4.92: In Exercises 9194, use the Trapezoidal Rule and Simpsons Rule with ...
 4.93: In Exercises 9194, use the Trapezoidal Rule and Simpsons Rule with ...
 4.94: In Exercises 9194, use the Trapezoidal Rule and Simpsons Rule with ...
Solutions for Chapter 4: Integration
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 4: Integration
Get Full SolutionsChapter 4: Integration includes 94 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. Calculus was written by and is associated to the ISBN: 9780547167022. This expansive textbook survival guide covers the following chapters and their solutions. Since 94 problems in chapter 4: Integration have been answered, more than 63172 students have viewed full stepbystep solutions from this chapter.

Annuity
A sequence of equal periodic payments.

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Conditional probability
The probability of an event A given that an event B has already occurred

Directed distance
See Polar coordinates.

Distance (on a number line)
The distance between real numbers a and b, or a  b

Gaussian curve
See Normal curve.

Identity
An equation that is always true throughout its domain.

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

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Interquartile range
The difference between the third quartile and the first quartile.

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Partial fraction decomposition
See Partial fractions.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Quadrantal angle
An angle in standard position whose terminal side lies on an axis.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Solve by substitution
Method for solving systems of linear equations.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Supply curve
p = ƒ(x), where x represents production and p represents price

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].