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M151groupfinalF06

# M151groupfinalF06 - Last Name First Name Instructor Math...

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Last Name: First Name: Instructor: Math 151 Group Final (Fall 2006) You are not allowed to use notes, books, calculators, personal stereos or cell phones. You have exactly two hours. Write clearly so that you can avoid mistakes and count on partial credits. Carry out the obvious simpli f cations so that you can display your answers in an easily readable manner. The following list is for the recording of the points only. Do not write your answersonth ispage . Points 1 /5 2/ 5 3/ 5 4/ 5 5/ 5 6 /10 7/ 10 8/ 10 9/ 10 10 / 5 11 / 10 12 / 10 13 / 5 14 / 5 Total: /100 1

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1 (5 pts.) Determine Z x cos ³ x 2 ´ dx 2 (5 pts.) Determine Z x 1 x 2 7 x +12 dx 2
3 (5 pts.) Determine Z sin 2 (3 x ) dx. 4 (5 pts.) Determine whether the improper integral Z 0 x ( x 2 +1) 2 dx converge or diverges, and its value in case it converges. 3

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5 (5 pts.) Use a comparison test to determine whether the improper integral Z 1 sin 2 ( x ) e x dx converges or diverges. 4
6 (10 pts.) Determine the volume of the solid that is obtained by revolving the region between the graph of f ( x )= r x x 2 +4 and the interval £ e 2 4 , e 3 4 ¤ about the x -axis.

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M151groupfinalF06 - Last Name First Name Instructor Math...

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