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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 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 n1)

The power rule of differentiation:

dduun=nun1+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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