   Chapter 12, Problem 25RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 1-26.(a) (b) ∫ ( x 2 − 1 ) 10 x d x (c) ∫ ( x 2 − 1 ) 7 3 x d x (d) ∫ ( x 2 − 1 ) − 2 / 3 x d x

(a)

To determine

To calculate: The value of the integral (x21)4xdx.

Explanation

Given Information:

The provided integral is (x21)4xdx.

Formula used:

According to the power formula of integrals, if u=u(x),

Then, undu=un+1n+1+C.

Calculation:

Consider the provided integral,

(x21)4xdx

Rewrite the integral by multiplying and dividing by 2 as,

12(x21)42xdx

Consider the power rule of integrals,

undu=un+1n+1+C

Now, to use the power rule, the integrand should have the function u(x) and its derivative u(x) where, n1.

Here,

u=x21, u=2x and n=4,

Since, all required values are present, so the integral is of the form,

12(x21)42xdx=12u4

(b)

To determine

To calculate: The value of the integral (x21)10xdx.

(c)

To determine

To calculate: The value of the integral (x21)73xdx.

(d)

To determine

To calculate: The value of the integral (x21)2/3xdx.

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