q5-sect7-F-2011

q5-sect7-F-2011 - PRINT Your Name: Quiz 5 — September 16,...

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Unformatted text preview: PRINT Your Name: 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.

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