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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.3, Problem 9QY
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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 n≠1)

The power rule of differentiation:

dduun=nun−1+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:

27∫7x+4(7dx)

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

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

Now apply, the power rule of integrals:

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Sect-5.1 P-1CPSect-5.1 P-2CPSect-5.1 P-3CPSect-5.1 P-4CPSect-5.1 P-5CPSect-5.1 P-6CPSect-5.1 P-7CPSect-5.1 P-8CPSect-5.1 P-1SWUSect-5.1 P-2SWU
Sect-5.1 P-3SWUSect-5.1 P-4SWUSect-5.1 P-5SWUSect-5.1 P-6SWUSect-5.1 P-7SWUSect-5.1 P-8SWUSect-5.1 P-9SWUSect-5.1 P-10SWUSect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-9ESect-5.1 P-10ESect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.1 P-42ESect-5.1 P-43ESect-5.1 P-44ESect-5.1 P-45ESect-5.1 P-46ESect-5.1 P-47ESect-5.1 P-48ESect-5.1 P-49ESect-5.1 P-50ESect-5.1 P-51ESect-5.1 P-52ESect-5.1 P-53ESect-5.1 P-54ESect-5.1 P-55ESect-5.1 P-56ESect-5.1 P-57ESect-5.1 P-58ESect-5.1 P-59ESect-5.1 P-60ESect-5.1 P-61ESect-5.1 P-62ESect-5.1 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P-3CPSect-5.5 P-4CPSect-5.5 P-5CPSect-5.5 P-6CPSect-5.5 P-1SWUSect-5.5 P-2SWUSect-5.5 P-3SWUSect-5.5 P-4SWUSect-5.5 P-5SWUSect-5.5 P-6SWUSect-5.5 P-7SWUSect-5.5 P-8SWUSect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.5 P-25ESect-5.5 P-26ESect-5.5 P-27ESect-5.5 P-28ESect-5.5 P-29ESect-5.5 P-30ESect-5.5 P-31ESect-5.5 P-32ESect-5.5 P-33ESect-5.5 P-34ESect-5.5 P-35ESect-5.5 P-36ESect-5.5 P-37ESect-5.5 P-38ESect-5.5 P-39ESect-5.5 P-40ESect-5.5 P-41ESect-5.5 P-42ESect-5.5 P-43ESect-5.5 P-44ESect-5.5 P-45ESect-5.5 P-46ESect-5.5 P-47ESect-5.5 P-48ESect-5.5 P-49ESect-5.5 P-50ESect-5.5 P-51ESect-5.5 P-52ESect-5.5 P-53ESect-5.5 P-54ESect-5.5 P-55ESect-5.5 P-56ESect-5.5 P-57ESect-5.5 P-58ESect-5.6 P-1CPSect-5.6 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