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# Solutions for Chapter 6: Applications of Definite Integrals

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

ISBN: 9780321587992

Solutions for Chapter 6: Applications of Definite Integrals

Solutions for Chapter 6
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##### ISBN: 9780321587992

Thomas' Calculus was written by and is associated to the ISBN: 9780321587992. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Since 42 problems in chapter 6: Applications of Definite Integrals have been answered, more than 11648 students have viewed full step-by-step solutions from this chapter. Chapter 6: Applications of Definite Integrals includes 42 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
• Acceleration due to gravity

g ? 32 ft/sec2 ? 9.8 m/sec

• Common ratio

See Geometric sequence.

• Complex plane

A coordinate plane used to represent the complex numbers. The x-axis of the complex plane is called the real axis and the y-axis is the imaginary axis

• Constant of variation

See Power function.

• Coterminal angles

Two angles having the same initial side and the same terminal side

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• Fibonacci sequence

The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

• First octant

The points (x, y, z) in space with x > 0 y > 0, and z > 0.

• First-degree equation in x , y, and z

An equation that can be written in the form.

• Identity

An equation that is always true throughout its domain.

• Inverse reflection principle

If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

• Line graph

A graph of data in which consecutive data points are connected by line segments

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Lower bound of f

Any number b for which b < ƒ(x) for all x in the domain of ƒ

• Positive angle

Angle generated by a counterclockwise rotation.

• Richter scale

A logarithmic scale used in measuring the intensity of an earthquake.

• Unit vector

Vector of length 1.

• Vertex of a parabola

The point of intersection of a parabola and its line of symmetry.

• Weighted mean

A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

• y-intercept

A point that lies on both the graph and the y-axis.