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# Solutions for Chapter 5: Integration

## Full solutions for Thomas' Calculus | 12th Edition

ISBN: 9780321587992

Solutions for Chapter 5: Integration

Solutions for Chapter 5
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##### ISBN: 9780321587992

Since 86 problems in chapter 5: Integration have been answered, more than 3964 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5: Integration includes 86 full step-by-step solutions. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992.

Key Calculus Terms and definitions covered in this textbook
• Arrow

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

• Binomial probability

In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once

• Constant

A letter or symbol that stands for a specific number,

• Deductive reasoning

The process of utilizing general information to prove a specific hypothesis

• equation of a hyperbola

(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1

• Even function

A function whose graph is symmetric about the y-axis for all x in the domain of ƒ.

• Exponent

See nth power of a.

• Fundamental

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

• Grapher or graphing utility

Graphing calculator or a computer with graphing software.

• Higher-degree polynomial function

A polynomial function whose degree is ? 3

• Identity properties

a + 0 = a, a ? 1 = a

• Irrational numbers

Real numbers that are not rational, p. 2.

• Left-hand limit of f at x a

The limit of ƒ as x approaches a from the left.

• Minute

Angle measure equal to 1/60 of a degree.

• Natural logarithmic regression

A procedure for fitting a logarithmic curve to a set of data.

• Odd function

A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).

• Periodic function

A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

• Relation

A set of ordered pairs of real numbers.

• Stretch of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.

• Symmetric property of equality

If a = b, then b = a

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