   Chapter 5, Problem 31RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Applying the General Power Rule In Exercises 21–32, find the indefinite integral. Check your result by differentiating. ∫ 2 7 x − 1   d x

To determine

To calculate: The indefinite integral 27x1dx.

Explanation

Given Information:

The provided indefinite integral is 27x1dx.

Formula used:

The power rule of integrals:

undu=un+1n+1+C (n1)

The power rule of differentiation:

ddxun=nun1+C

Calculation:

Consider the indefinite integral:

27x1dx

Let u=7x1, then derivative will be,

du=d(7x1)=7dx

Rewrite integration as,

27x1dx=27(7x1)1/27dx

Substitute du for 7dx and u for 7x1 in provided integration.

27(7x1)1/27dx=27u1/2du

Now apply, the power rule of integrals:

27

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