11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Verifying a Formula In Exercises 33-36, use the method of partial fractions to verify the integration formula.

∫ 1 a 2 − x 2 d x = 1 2 a ln | a + x a − x | + C

To determine

To prove: The solution of the integral ∫1a2−x2dx=12aln|a+xa−x|+C specified using partial fractions.

The integral is ∫1a2−x2dx=12aln|a+xa−x|+C.

Consider the specified integral:

Use partial fractions express the integrant as follow:

1a2−x2=1(a+x)(a−x)=Aa+x+Ba−x1=A(a−x)+B(a+x)

Substitute x=a as follows:

1=B(2a)B=12a

Substitute x=−a as follows:

1=A(−2a)A=−12a

Now, solve as shown below:

Check out a sample textbook solution.

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Verifying a Formula In Exercises 33-36, use the method of partial fractions to verify the integration formula.

∫ 1 a 2 − x 2 d x = 1 2 a ln | a + x a − x | + C

Chapter 8 Solutions

Additional Math Solutions

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Solutions

Calculus (MindTap Course List)

Verifying a Formula In Exercises 33-36, use the method of partial fractions to verify the integration formula. ∫ 1 a 2 − x 2 d x = 1 2 a ln | a + x a − x | + C

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Calculus Calculus (MindTap Course List)11th Edition

Verifying a Formula In Exercises 33-36, use the method of partial fractions to verify the integration formula.

∫ 1 a 2 − x 2 d x = 1 2 a ln | a + x a − x | + C