exam3 - APPM 2350 EXAM 3 FALL 2007 INSTRUCTIONS Computers...

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APPM 2350 EXAM 3 FALL 2007 INSTRUCTIONS: Computers, calculators, books, and crib sheets are not permitted. Write your (1) name, (2) instructor’s name, and (3) recitation number on the front of your bluebook. Work all problems. Show your work clearly. Note that a correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. 1. (25 points) A Calculus III student is trying to determine the moment about the x -axis of a plate with mass density ρ ( x, y ) (mass per unit area). She determines that the desired moment can be calculated by evaluating the integral M x = Z 1 y =0 Z 1 x = 3 y sin( πx 2 ) x 2 dx dy and she correctly notes that the integral can’t be evaluated in its present form. She then decides to change the order of integration. (a) What function ρ ( x, y ) describes the density of the material? (b) Sketch the region of integration (ie. the shape of the plate) and clearly indicate the axis, boundaries, intersection points, etc. (c) Rewrite the integral by switching the order of integration.
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