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Quiz 5 — September 16, 2011 – Section 7 – 10:10 – 11:00
Remove everything from your desk except a pencil or pen.
Circle your answer. Show your work.
coherent. CHECK your answer.
The quiz is worth 5 points. Your work should be correct and √
arctan xdx.
√
1
Answer: Let w = x. It follows that dw = 2√x dx. In other words, 2wdw = dx.
The original integral is 2 w arctan wdw. We use integration by parts. Let u =
2
dw
arctan w and dv = w. We compute du = 1+w2 and v = w . The original integral
2
is:
w2
w2
w2 dw
2
= w2 arctan w −
arctan w −
dw
2
2 1 + w2
1 + w2
Find = w2 arctan w − 1
dw = w2 arctan w − w + arctan w + C
1 + w2
√
√
= (x + 1) arctan x − x + C .
1− Check: The derivative of the proposed answer is:
√
√
1
1
+ arctan x − √ = arctan x.
(x + 1) √
2 x(1 + x)
2x 1 ...
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This note was uploaded on 10/12/2011 for the course MATH 142 taught by Professor Kustin during the Fall '11 term at South Carolina.
 Fall '11
 KUSTIN

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