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

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Chapter 5.1, Problem 26E
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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 25-36, find the indefinite integral. Check your result by differentiating. See Examples 4 and 5.

∫ ( 5 − x )   d x

To determine

To calculate: The indefinite integral ∫(5−x)dx and verify the result by differentiation.

Explanation

Given Information:

The provided indefinite integral is ∫(5−x)dx.

Formula used:

The integration and differentiation formulae used are:

1. ddx[(f(x)±g(x))]=f′(x)+g′(x)

2. ∫k dx=kx+ C

3. ∫xn dx=xn+1n+1+ C

4. ddx[kx]=k

5. ddx[xn]=nxn−1

Here, C is the constant of integration.

Calculation:

Consider the indefinite integral ∫(5−x)dx.

Hence,

∫(5−x)dx=∫5dx−∫xdx

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

∫(5−x)dx=∫5dx−∫xdx=5x−[x1+12]+C=5x−x22+C

Thus, the indefinite integral is evaluated as 5x−x22+C

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