   Chapter 5.1, Problem 36E ### 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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# Finding indefinite integrals In Exercises 25–36, find the indefinite integral. Check your result by differentiating. See Examples 4 and 5. ∫ 14 x − 3 x 4   d x

To determine

To calculate: The value of indefinite integral (14x3x4)dx and check the result by differentiation.

Explanation

Given Information:

The indefinite integral is (14x3x4)dx.

Formula used:

The simple power rule of integration, xndx=xn+1n+1+C where, n1.

The sum or difference rule of integration, (f(x)±g(x))dx=f(x)dx±g(x)dx.

The simple power rule for the derivative, ddx[xn]=nxn1.

Calculation:

Consider the indefinite integral (14x3x4)dx.

The integrand of the indefinite integral is (14x3x4).

Integrate the provided indefinite integral use the sum or difference rule of integration, (f(x)±g(x))dx=f(x)dx±g(x)dx.

(14x3x4)dx=(14xx4)dx+(3x4)dx=14(xx14)dx3(1x14)dx=14(x114)dx3(x14)dx=14(x34)dx3(x14)dx

Integrate further, integral use the simple power rule of integration, xndx=xn+1n+1+C

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