math20b - Name: PID: TA: Sec. No: Sec. Time: Math 20B....

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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20B. Midterm Exam 1 January 30, 2008 Turn off and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. 1. Evaluate the following integrals e2 (a) (3 points) e (b) (3 points) 1 dx x ln(x) √ x x − 2 dx # 1 2 3 4 Σ Points 6 6 6 6 24 Score √ 2. A particle initially at the origin moves along the x-axis with velocity v (t) = (2 − t) t. (a) (3 points) Find the particle’s position at time t = 4. (b) (3 points) What is the total distance traveled by the particle during the time interval from t = 0 to t = 4? (Be careful!) 3. (6 points) Find the area of the region bounded by the curves y = cos(x), y = cos(2x), the y -axis and the line x = π . 1 cos x cos 2x Π 2 1 Π 4. (6 points) Let R denote the region bound by the curves y = x3 and y 2 = x. For each of the following solids, write down (but do not evaluate) a definite integral that computes its volume: (a) The solid obtained by rotating R about the x-axis (b) The solid obtained by rotating R about the y -axis (c) The solid whose base is R and whose cross-sections parallel to the y -axis are squares. ...
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This note was uploaded on 08/31/2011 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.

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math20b - Name: PID: TA: Sec. No: Sec. Time: Math 20B....

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