Math 1100-006
§12.2 Integration by Substitution
Homework Worksheet
Answer the questions in the spaces provided. If you run out of room for an
answer, you may attach additional sheets of paper. You must show all of
your work to receive full points. Staple this worksheet to the rest of the
assignment.
Name:
1. Three integrals are given in parts (a)-(c). You can integrate one of them using the
techniques we have learned. In the other two cases, give one guess at what the usubstitution should be, and explain why it doesn’t work.
Z
x5
(a)
dx
(3x5 + 3)2
Z
(b)
x4 + 1
dx
(3x5 + 3)2
Z
(c)
x4
dx
(3x5 + 3)2
(d) Give your own example of an integral that looks as though it might use u-substitution
but that cannot be integrated using the methods we have studied so far. Explain
why it cannot be integrated.
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