   Chapter 12.2, Problem 1CP ### 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

# Which of the following can be evaluated with the Power Rule? (a)  ∫ ( 4 x 2 + 1 ) 10 ( 8 x d x ) (b)  ∫ ( 4 x 2 + 1 ) 10 ( x d x ) (c)  ∫ ( 4 x 2 + 1 ) 10 ( 8 d x ) (d)  ∫ ( 4 x 2 + 1 ) 10 d x

To determine

Which integral can be evaluated with the help of power rule. If the provided options are given below,

(a)(4x2+1)10(8x)dx(b)(4x2+1)10(x)dx(c)(4x2+1)108dx(d)(4x2+1)10dx

Explanation

Given Information:

The provided options are

(a)(4x2+1)10(8x)dx(b)(4x2+1)10(x)dx(c)(4x2+1)108dx(d)(4x2+1)10dx

Explanation:

Consider the option (a), (4x2+1)10(8x)dx

Use the power rule undu=un+1n+1+C, if u=u(x) and the derivative of u is u(x) and n1.

Here,

u=4x2+1

Then, on obtaining differentials,

du=8x

Since, there is presence of the factor x in the term 8x of the provided integral.

Therefore, the power rule can be used to evaluate the provided integral.

Now consider the option (b), (4x2+1)10(x)dx

Rewrite the provided integral by dividing and multiplying by 8 as,

18(4x2+1)10(8x)dx

Use the power rule undu=un+1n+1+C, if u=u(x) and the derivative of u is u(x) and n1

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