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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 x 2 1 x 3 d x

To determine

To calculate: The indefinite integral of 3x21x3 dx and to check the result by differentiating.

Explanation

Given Information:

The provided expression is 3x21x3 dx.

Formula used:

General Power Rule:

If u is a differentiable function of x, then

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

The Constant Multiple Rule:

ddxcf(x)=cf(x)

The Chain Rule:

ddxf(g(x))=f(g(x))g(x)

The Power Rule:

ddxxn=nxn1

Where n is a real number.

Calculation:

Consider 3x21x3 dx,

This can be written as 3x2(1x3)12dx.

Let u=1x3,

So,

dudx=3u2

Now use the general power rule to get,

(u)12du

Now the integral will be:

u12+112+1+C=u1212+C=2

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