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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20E. Midterm Exam 2 November 21, 2008 Turn off and put away your cell phone. You may use one page of notes, but no calculators, books or other assistance. 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. # Points Score 1 8 2 16 3 22 Σ 46 1. Consider the double integral integraldisplay 2 integraldisplay 4 2 y e x 2 +1 dx dy. a. (3 points) Draw a careful sketch of the region of integration, clearly labeling all bounding curves. Solution: The region is the triangle with vertices (0 , 0), (4 , 0), and (4 , 2). b. (5 points) Change the order of integration and evaluate the integral. Solution: integraldisplay 2 integraldisplay 4 2 y e x 2 +1 dx dy = integraldisplay 4 integraldisplay 1 2 x e x 2 +1 dy dx = integraldisplay 4 1 2 xe x 2 +1 dx = 1 4 ( e 17 − e ) . 2. Consider the triple integral integraldisplayintegraldisplayintegraldisplay W radicalbig x 2 + y 2 + z 2 dV, where W is the solid region lying above the...
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This note was uploaded on 04/21/2010 for the course MATH 20E taught by Professor Enright during the Winter '07 term at UCSD.
 Winter '07
 Enright
 Math, Vector Calculus

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