Integration By Parts - Worksheet 5.4 Page 3

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Calculus Maximus
WS 5.4: Integration by Parts
6. Evaluate the following definite integrals. Show the antiderivative. Verify on your calculator.
1
2
x
(a)
t
sin 3
tdt
(b)
x
1
e dx
0
0
e
1
3
ln
x
r
 )
3
2
(c)
dx
(d)
dr
(Hint: let
r
r
r
2
2
x
4
r
1
0
dy
y  when
x  .
2
7. Solve:
x
sec
x
and
1
0
dx
 
8. Find the area of the region enclosed by the x-axis and the curve
for
.
y
x
sin
x
x
2
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