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Unformatted text preview: Name: TA: Math 20B. Midterm Exam 1 January 30, 2009 Sec. No: PID: Sec. Time: Turn oﬀ and put away your cell phone. You may use one page of notes, but no books, calculators, or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clariﬁcation. # 1 2 3 4 Σ Points 7 6 6 6 25 Score 1. Evaluate the given expression: (a) (2 points) x2 cos(x3 + 1) dx 2 (b) (3 points)
0 x3 (x2 + 1)1/2 dx d (c) (2 points) dx x2 ecos t dt
0 2. A particle moving along a straight line has velocity v (t) = t2 − 2t. (a) (3 points) Find the average velocity of the particle on the interval 0 ≤ t ≤ 4. (b) (3 points) Find the net change in position (displacement) of the particle over the interval 0 ≤ t ≤ 4. 3. Let R be the region bounded by the curves y = x2 and y = 3x. (a) (3 points) Write down (but do not evaluate) a deﬁnite integral that equals the area of R. (b) (3 points) Write down (but do not evaluate) a deﬁnite integral that equals the volume of the solid obtained by revolving R about the line x = −1. 4. (a) (2 points) Write down (but do not evaluate) a deﬁnite integral that equals the area of the region which lies outside the curve r = 2 − 2 sin(θ) and inside the circle r = 2.
2 1 3 2 1 1 2 3 1 2 3 4 (b) (4 points) Evaluate the integral from part (a). ...
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This note was uploaded on 01/26/2010 for the course MATH 02 taught by Professor Lindblad during the Winter '20 term at UCSD.
 Winter '20
 lindblad
 Math

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