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

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Chapter 5.1, Problem 23E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Rewriting Before Integrating In Exercises 19-24, find the indefinite integral. See Example 3.

Original Integral Rewrite Integrate Simplify

∫ 1 2 x 3 d x

To determine

To calculate: The indefinite integral ∫12x3⋅dx by rewriting it before.

Explanation

Given Information:

The indefinite integral ∫12x3⋅dx

Formula used:

The power rule of the integration is

∫xn⋅dx=xn+1n+1+C,       n≠−1

The constant multiple rule of the integration is

∫k⋅f(x)⋅dx=k⋅∫f(x)⋅dx

Calculation:

Consider the provided indefinite integral,

∫12x3⋅dx

Use constant multiple rule of integration and rewrite the above integral in the form ∫xn⋅dx,

∫12x3⋅dx=∫12×1x3⋅dx=12×∫1x3⋅dx=12∫x−3⋅dx

Use power rule of integration and integrate the above integral as follows:

12∫x−3⋅dx=12[

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