172 FALL 2009 EXAM 1

# 172 FALL 2009 EXAM 1 - Hooke’s law f x = kx 5 4(10 pts Find the area bounded between the curves y = √ x and y = x 2 5(10 pts Find the volume of

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1 Math 172 Exam #1 September 29, 2009 Name: Section#: Signature: ID# Instructions: Do all the problems. Circle your answers. To get credit, you need to show your work. The answer alone will not be counted as a solution. 1. (10 pts each) Evaluate each of the following integrals: (a) Z x x 2 - x - 2 dx

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2 (b) Z 1 - x 2 dx . Hint: Consider a substitution: x = sin θ. (c) Z sin 3 x cos xdx
3 2. (10 pts each) Evaluate each of the following improper integrals: (Hint: A limit relationship?) (a) Z 1 x 2 ln xdx

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4 (b) 1 Z 0 1 x 1 / 2 dx 3. (10pts) A force of 10 N is required to maintain a spring stretched from its natural length of 1m to a length of 2m. How much work is done in stretching the spring from 2m to 3m? (Hint:

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Unformatted text preview: Hooke’s law: f ( x ) = kx .) 5 4. (10 pts) Find the area bounded between the curves y = √ x and y = x 2 . 5. (10 pts) Find the volume of the solid generated by rotating the region bounded by the curves y = √ x and y = x 2 about the x-axis. 6 6. (10 pts) Use the method of cylindrical shells to ﬁnd the volume of the solid generated by rotating the region bounded by the curves y = √ x and y = x 2 about the y-axis. 7. (10 pts) Find the length of the curve: y = 2 3 ( x-2) 3 / 2 , 3 ≤ x ≤ 4....
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## This note was uploaded on 05/12/2010 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

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172 FALL 2009 EXAM 1 - Hooke’s law f x = kx 5 4(10 pts Find the area bounded between the curves y = √ x and y = x 2 5(10 pts Find the volume of

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