Evaluate the following integrals or show that they are divergent:
(a)
(b)
Solution:
(a)
ExpandStep 1:
|
First, we write
|
|
Now, we use integration by parts.
|
Let and
|
Then, and
|
Using integration by parts, we get
|
|
ExpandStep 2:
|
Now, using L'Hopital's Rule, we get
|
|
(b)
ExpandStep 1:
|
First, we write
|
|
Now, we use integration by parts.
|
Let and
|
Then, and
|
Using integration by parts, we get
|
|
ExpandStep 2:
|
Now, using L'Hopital's Rule, we get
|
|
|
ExpandFinal Answer:
|
(a)
|
(b)
|
Return to Sample Exam