math_172_(fall_2008)_exam1spring07

math_172_(fall_2008)_exam1spring07 - For full credit, any...

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Math 172: Second Semester Calculus Spring Semester, 2007 First Exam # 1 2 3 4 5 6 total worth 15 20 10 15 20 20 100 score N a m e : S e c t i o n : ID Number: Instructions: Work must be shown to receive credit. No calculators. Question 1. (15 points) Find the area of the region enclosed by the curves y = 3 x and y = 2 / x.
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Question 2. (5 points each) Compute the following integrals. (A) dx x x ) ln( (B) dx x x ) ( tan ) ( sec 3 2 (C) + 2 1 2 2 1 dx x x (D) π 0 ) sin( 2 dx x x
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Question 3. (10 points ) Use any method to evaluate the indefinite integral dx x x 2 3 4
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Question 4. (5 points each) Evaluate the following improper integrals, indicating if any of them diverges.
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Unformatted text preview: For full credit, any improper integral must be re-interpreted as an appropriate limit. A) 1 2 1 dx x B) 1 3 / 1 1 dx x C) e dx x x ln 1 Question 5. (20 points) Let R be the region bounded by x = 0, x = 1, y = x 2 + 1 and the x-axis. R Find the volume of the object obtained by spinning R about the x axis . Question 6. (20 points) Let R be the same region as in question 5, i.e. bounded by x = 0, x = 1, y = x 2 + 1 and the x-axis. R Find the volume of the object obtained by spinning R about the y -axis....
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math_172_(fall_2008)_exam1spring07 - For full credit, any...

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