Common Exam 1 M175 Worksheet - 2016 Page 4
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1
2
3
4Part II: Long Form
Show all work. Unsupported answers will not receive full credit.
Present your work clearly with correct notation. Neatness counts.
Read the specific instructions for each problem.
8. (10 pts.) Transform the antiderivative
2
2
1
using the trig substitution
= sin . Simplify the new integral until there are no square roots.
9. (10 pts.) Compute the integral
1
3
2
0
10. (10 pts.) Find the antiderivative
1
2
2
3
2
11. (10 pts.) Compute the improper integral
1
1 5
9
12. (10 pts.) The antiderivative
3
2
2
cos(
)
can be computed successfully by starting with either of two methods:
2
2
2
Substitution with
=
or Parts with
=
and
= 2 cos(
)
.
Pick your favorite. Solve the problem completely.
Suggestion: Work on scratch paper until you make up your mind what works. Then write
up your answer on the test paper.
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