   Chapter 5.2, Problem 33E ### 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 9–34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5. ∫ − 3 2 t + 3   d t

To determine

To calculate: The indefinite integral of 32t+3dt and check the result by differentiating.

Explanation

Given Information:

The indefinite integral is 32t+3dt.

Formula used:

General Power Rule:

If u is a differentiable function of x, then

undudxdx=undu=un+1n+1+c,n1

The Power Rule:

ddttn=ntn1

Where n is a real number.

Calculation:

Consider indefinite integral,

32t+3dt

The above indefinite integral 32t+3dt can be written as 3(2t+3)12dt.

Let u=2t+3,

So,

du=2 dt

Now use the general power rule to get,

3(2t+3)12dt=32(u)12du

Now the integral will be:

32(u)12du=32u12+1x

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