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

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Chapter 5, Problem 1RE
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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
3 views

Finding Indefinite Integrals In Exercises 1–14, find the indefinite integral. Check your result by differentiating.

∫ 16   d x

To determine

To calculate: The indefinite integral ∫16dx.

Answer

Solution:

The indefinite integral ∫16dx is 16x+C_.

Explanation

Given Information:

The provided indefinite integral is ∫16dx.

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:

∫16dx

Rewrite as,

∫16x0dx

Now apply, the power rule of integrals:

∫16x0dx=16(x0+10+1)+C=16x+C

Now, check this value by differentiating it using the power rule:

ddx(16x+C)=16+0=16

Since, the value obtained after the derivative matches the integrand. So, it is correct.

Therefore, the indefinite integral ∫16dx is 16x+C.

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