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# Solutions for Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION

## Full solutions for Calculus: Early Transcendentals, | 10th Edition

ISBN: 9780470647691

Solutions for Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION

Solutions for Chapter 5.9
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##### ISBN: 9780470647691

Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 74 problems in chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION have been answered, more than 38325 students have viewed full step-by-step solutions from this chapter. Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION includes 74 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Coefficient

The real number multiplied by the variable(s) in a polynomial term

• Coefficient matrix

A matrix whose elements are the coefficients in a system of linear equations

• Combinatorics

A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

• De Moivre’s theorem

(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

See Polynomial function in x

• Logarithmic regression

See Natural logarithmic regression

• Mean (of a set of data)

The sum of all the data divided by the total number of items

• Natural logarithm

A logarithm with base e.

• nth root

See Principal nth root

• Octants

The eight regions of space determined by the coordinate planes.

• Rational numbers

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

• Solve a system

To find all solutions of a system.

• Solve by substitution

Method for solving systems of linear equations.

• Standard form: equation of a circle

(x - h)2 + (y - k2) = r 2

• Sum of an infinite series

See Convergence of a series

• Summation notation

The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

• Vertical asymptote

The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.

• Vertical translation

A shift of a graph up or down.

• Weights

See Weighted mean.

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