Question
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Use a change of variables to evaluate the following indefinite integral.

Determine a change of variables from to u. Choose the correct answer below.
A.
B.
C.
D.
Write the integral in terms of .
du
Evaluate the integral.

Ask by Schofield Schneider. in the United States
Mar 09,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Let . Then, the integral becomes , which evaluates to . Substituting back, the answer is .

Solution

Let . Notice that
so differentiating with respect to we have
which implies
Substituting into the original integral
we replace with and :
This shows that option D, , is the correct substitution.
Now, evaluating the integral:
Substituting back , we obtain
Thus, the evaluated integral is

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

To evaluate the given integral using a change of variables, let’s choose (Option D). This means that and . The differential can be expressed as .
Now, substitute everything into the integral. The integrand becomes:
Thus, we have:
Now, let’s evaluate the integral:
Finally, substituting back for :

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