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

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Chapter 5.1, Problem 16E
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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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Finding Indefinite Integrals In Exercises 7-18, find the indefinite integral Check your result by differentiating. See Examples 1 and 2.

∫ 8 y − 5   d y

To determine

To calculate: The indefinite integral ∫8y−5dy and verify the result by differentiation.

Explanation

Given Information:

The provided indefinite integral is ∫8y−5dy.

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]=nxn−1

Here, C is the constant of integration.

Calculation:

Consider the indefinite integral ∫8y−5dy.

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

∫8y−5dy=8[y−5+1−4]+C=−2y−4+C

Thus, the indefinite integral is evaluated as −2y−4+C

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