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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 7-18, find the indefinite integral Check your result by differentiating. See Examples 1 and 2.

v 1 / 2 d v

To determine

To calculate: The indefinite integral v12dv and verify the result by differentiation.

Explanation

Given Information:

The provided indefinite integral is v12dv.

Formula used:

The integration and differentiation formulae used are:

1. ddx[(f(x))]=f(x)

2. k dx=kx+ C

3. xn dx=xn+1n+1+ C

4. ddx[(f(x))]=f'(x)

5. ddx[kx]=k

6. ddx[xn]=nxn1

Here, C is the constant of integration.

Calculation:

Consider the indefinite integral v12dv.

Now, use the formulae k dx=kx+C and xn dx=xn+1n+1+C to evaluate the integral as:

v12dv=[v12+112+1]+C=v1212+C=2v12+C

Thus, the indefinite integral is evaluated as 2v12+C

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