math_172_(fall_2008)_exam1spring08

# math_172_(fall_2008)_exam1spring08 - R about the y axis R...

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Math 172: Second Semester Calculus Spring Semester, 2008 Make-up Exam 1 # 1 2 3 4 5 6 Total worth 13 15 15 24 15 18 100 s c o r e 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. (13 points) Find the area of the region bounded by the curve x y 1 = and the lines x y = and 2 = x .

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Question 2. (15 points) The region R is bounded by the curve y = 1/ x where x ranges from 1 to 3 and the x axis. Find the volume of the solid object obtained by rotating R about the x axis . R
Question 3 ( 15 points ) The region R is bounded by the curve y = sin x where x ranges from 0 to π and the x axis. Find the volume of the solid object obtained by rotating

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Unformatted text preview: R about the y axis . R Question 4. (6 points each) Evaluate the following integrals (A) âˆ« dx x x ) ( sec ) tan( 3 (B) âˆ« âˆ’ + dx x x ) 5 )( 3 ( 2 (C) âˆ« 2 / ) 2 cos( Ï€ dx x x (D) âˆ« âˆ’ dx x ) ( tan 1 Question 5. (15 points) Evaluate the following integral ( ) âˆ« âˆ’ + dx x 2 / 3 2 9 Î¸ Question 6. (6 points each) Express the following improper integrals as the appropriate limits. Are they convergent or divergent? If divergent, explain why. If convergent, evaluate. (A) âˆ« 1 3 / 1 1 dx x (B) âˆ« âˆž âˆ’ 2 3 dx e x (C) âˆ« âˆž e dx x x 2 )) (ln(...
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## This note was uploaded on 02/14/2011 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

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math_172_(fall_2008)_exam1spring08 - R about the y axis R...

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