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# Test3s - MATH 1501 Test 3 November 9 2009 No books or notes...

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MATH 1501 Test 3 November 9, 2009 No books or notes allowed. No laptop, graphic calculator or wireless devices allowed. Write clearly. Show your work and justify your answers. Remember to add your name to every page. Name: Question: 1 2 3 4 Total Points: 26 25 24 25 100 Score:

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MATH 1501 Test 3 November 9, 2009 1. Evaluate the following deﬁnite integrals. (a) (13 points) Z 1 0 ( x + 2) 2 - 4 x dx Solution: Z 1 0 ( x + 2) 2 - 4 x dx = Z 1 0 x 2 + 4 x x dx = Z 1 0 ( x + 4) dx = 1 2 + 4 (b) (13 points) Z 1 0 ( x + 1) 2 p 3 + ( x + 1) 3 dx Solution: Calling u = 3 + ( x + 1) 3 we get du = 3( x + 1) 2 dx . Thus Z 1 0 ( x + 1) 2 p 3 + ( x + 1) 3 dx = 1 3 Z 11 4 udu = 2 9 u 3 2 11 4 = 2 9 (11 11 - 8) Name: Page 1 of 4
MATH 1501 Test 3 November 9, 2009 2. Evaluate the following indeﬁnite integrals. (a) (13 points) Z sin( x ) cos( x ) ( cos 2 ( x ) - sin 2 ( x ) ) dx Solution: Z sin( x ) cos( x ) ( cos 2 ( x ) - sin 2 ( x ) ) dx = 1 2 Z sin(2 x ) cos(2 x ) dx = 1 8 sin 2 (2 x )+ C Alternatively call

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Test3s - MATH 1501 Test 3 November 9 2009 No books or notes...

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