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Calculus II Test
#3 April
19, 2004
Name____________________ R. Hammack Score
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(1) Find the following integrals.
(a)
(b)
tan(x) - x
+ C
(c)
(d)
Now we use integration by parts a second
time on the most recent integral.
Plugging THIS back into the first line gives
From this we get
so
(e)
(f)
(g)
Converting the above expression back to x,
we get:
(h)
(i)
Set x = -6, get 2(-6)+10
= -2B ====> B=1
Set x = -4, get 2(-4)+10
= 2A ====> A=1
(j)
Doing the long division:
Therefore
(2) Evaluate the following improper
integrals.
(a)
(b)
(3) Evaluate the limits.
(a)
NOTE: This is NOT an indeterminate form, so L'Hopital's Rule does not apply
(b)