Calculus II 
Quiz #7

April 12, 2002

Name____________________ 
R. Hammack

Score ______

(1) Evaluate the following improper integrals. Please show all of your
work.
(a)
0 + 1/8 = 1/8
(b)
We are going to have to find an antiderivative of ln x, so let's start off doing
that by integration by parts.
u = ln x dv
= dx
du = 1/x dx v = x
Now notice that has
an infinite discontinuity at 0. Therefore
[1]
+
+ 0 =
This last limit is an indetrerminate form ∞/∞, so applying L'Hopital's
rule gives a final answer of
=
[l]
= 1
(2) This limit has indeterminate form 0/0, so we can use L'Hopital's
rule to get 3
(0)
= 3