 4.1: Riemann sums are a way of approximating the area under a curve by u...
 4.2: If a and b are both negative, then is negative. [4.3]
 4.3: For any continuous function f defined over it follows that [4.4]
 4.4: Every integral can be evaluated using integration by parts. [4.6]
 4.5: Match each integral in column A with the corresponding antiderivati...
 4.6: Match each integral in column A with the corresponding antiderivati...
 4.7: Match each integral in column A with the corresponding antiderivati...
 4.8: Match each integral in column A with the corresponding antiderivati...
 4.9: Match each integral in column A with the corresponding antiderivati...
 4.10: Match each integral in column A with the corresponding antiderivati...
 4.11: Business: total cost. The marginal cost, in dollars, of producing t...
 4.12: Evaluate. [4.1]
 4.13: Evaluate. [4.1]
 4.14: Evaluate. [4.1]
 4.15: Find the area under the curve over the indicated interval. [4.3]
 4.16: Find the area under the curve over the indicated interval. [4.3]
 4.17: In each case, give an interpretation of the shaded region. [4.2, 4.3]
 4.18: In each case, give an interpretation of the shaded region. [4.2, 4.3]
 4.19: Evaluate. [4.3, 4.4]
 4.20: Evaluate. [4.3, 4.4]
 4.21: Evaluate. [4.3, 4.4]
 4.22: Evaluate. [4.3, 4.4]
 4.23: Evaluate. [4.3, 4.4]
 4.24: Decide whether is positive, negative, or zero. [4.3]
 4.25: Decide whether is positive, negative, or zero. [4.3]
 4.26: Decide whether is positive, negative, or zero. [4.3]
 4.27: Find the area of the region bounded by [4.4]
 4.28: Evaluate using substitution. Do not use Table 1. [4.5]
 4.29: Evaluate using substitution. Do not use Table 1. [4.5]
 4.30: Evaluate using substitution. Do not use Table 1. [4.5]
 4.31: Evaluate using substitution. Do not use Table 1. [4.5]
 4.32: Evaluate using integration by parts. Do not use Table 1. [4.6]
 4.33: Evaluate using integration by parts. Do not use Table 1. [4.6]
 4.34: Evaluate using integration by parts. Do not use Table 1. [4.6]
 4.35: Evaluate using integration by parts. Do not use Table 1. [4.6]
 4.36: Evaluate using Table 1. [4.7]
 4.37: Evaluate using Table 1. [4.7]
 4.38: Evaluate using Table 1. [4.7]
 4.39: Evaluate using Table 1. [4.7]
 4.40: Evaluate using Table 1. [4.7]
 4.41: Evaluate using Table 1. [4.7]
 4.42: Business: total cost. Refer to Exercise 11. Calculate the total cos...
 4.43: Find the average value of over [4.4]
 4.44: A particle starts out from the origin. Its velocity in mph after t ...
 4.45: Business: total revenue. A company estimates that its revenue will ...
 4.46: Integrate using any method. [4.34.6]
 4.47: Integrate using any method. [4.34.6]
 4.48: Integrate using any method. [4.34.6]
 4.49: Integrate using any method. [4.34.6]
 4.50: Integrate using any method. [4.34.6]
 4.51: Integrate using any method. [4.34.6]
 4.52: Integrate using any method. [4.34.6]
 4.53: Integrate using any method. [4.34.6]
 4.54: Evaluate. [4.54.7]
 4.55: Evaluate. [4.54.7]
 4.56: Evaluate. [4.54.7]
 4.57: Evaluate. [4.54.7]
 4.58: Evaluate. [4.54.7]
 4.59: Evaluate. [4.54.7]
 4.60: Evaluate. [4.54.7]
 4.61: Evaluate. [4.54.7]
 4.62: Use a graphing calculator to approximate the area between the follo...
Solutions for Chapter 4: Integration
Full solutions for Calculus and Its Applications  10th Edition
ISBN: 9780321694331
Solutions for Chapter 4: Integration
Get Full SolutionsChapter 4: Integration includes 62 full stepbystep solutions. Since 62 problems in chapter 4: Integration have been answered, more than 24372 students have viewed full stepbystep solutions from this chapter. Calculus and Its Applications was written by and is associated to the ISBN: 9780321694331. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus and Its Applications, edition: 10.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Boundary
The set of points on the “edge” of a region

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Constant term
See Polynomial function

Cube root
nth root, where n = 3 (see Principal nth root),

Distributive property
a(b + c) = ab + ac and related properties

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

Identity function
The function ƒ(x) = x.

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

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Natural numbers
The numbers 1, 2, 3, . . . ,.

Response variable
A variable that is affected by an explanatory variable.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Singular matrix
A square matrix with zero determinant

Terms of a sequence
The range elements of a sequence.

Union of two sets A and B
The set of all elements that belong to A or B or both.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.