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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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In Exercises 1-9, find the indefinite integral. Check your result by differentiating.

2 7 x + 4 d x

To determine

To calculate: The indefinite integral 27x+4dx.

Explanation

Given Information:

The provided indefinite integral is 27x+4dx.

Formula used:

The power rule of integrals:

undu=xn+1n+1+C (for n1)

The power rule of differentiation:

dduun=nun1+C

Calculation:

Consider the indefinite integral:

27x+4dx

Let u=7x+4, then derivative will be,

du=d(7x+4)=7dx

Rewrite above indefinite integration as:

277x+4(7dx)

Substitute du for 7dx and u for 7x+4 in provided integration.

277x+4(7dx)=27u1/2du=27(u1/2+132)+C=4u3221+C

Now apply, the power rule of integrals:

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