AP Calculus BC : Substitution of Variables (by parts and simple partial fractions)

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

Example Question #61 : Integrals

Possible Answers:

Correct answer:

Explanation:

In order to evaluate this integral, we will need to use partial fraction decomposition.

Multiply both sides of the equation by the common denominator, which is

This means that  must equal 1, and

The answer is .

Example Question #62 : Integrals

Integrate:

Possible Answers:

Correct answer:

Explanation:

To integrate, we must first make the following substitution:

Rewriting the integral in terms of u and integrating, we get

The following rule was used to integrate:

Finally, we replace u with our original x term:

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