Integration By Parts - Worksheet 5.4 Page 2
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4Calculus Maximus
WS 5.4: Integration by Parts
4. The graph of
y
f x
conforms to the slope field for
dy
the differential equation
4 ln
x
x
, as shown. Which
dx
of the following could be
f x ?
x
2
2
(A)
2
x
ln
3
x
3
(B)
x
ln
3
2
2
(C)
2
x
ln
x x
3
2
(D)
2
x
3 ln
x
1
3
4ln
x
2
x
(E)
2 ln
x
3
3
Short Answer
5. Evaluate the following integrals.
x
2
1
(a)
xe dx
(b)
x
sin
x dx
(c)
sin
xdx
2
(d)
ln xdx
(e) arctan 4tdt
Page 2 of 4
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