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

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Chapter 5.1, Problem 30E
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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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Finding indefinite integrals In Exercises 25–36, find the indefinite integral. Check your result by differentiating. See Examples 4 and 5.

∫ ( x 3 + 4 x + 2 )   d x

To determine

To calculate: The value of indefinite integral ∫(x3−4x+2)dx and check the result by differentiation.

Explanation

Given Information:

The indefinite integral is ∫(x3−4x+2)dx.

Formula used:

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

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]=nxn−1.

Calculation:

Consider the indefinite integral ∫(x3−4x+2)dx.

The integrand of the indefinite integral is (x3−4x+2).

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

∫(x3−4x+2)dx=∫x3dx−∫4xdx+∫2dx

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

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