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Unformatted text preview: MATH 32B PRACTICE MIDTERM October, 22nd, 2007 Problem 1. Consider the integral I = -2 0 f (x, y)dxdy, where f (x, y) = ex -y . Divide the rectangle [-2, 0] [0, 2] into 4 equal squares. Let L be the Riemann sum corresponding to this subdivision and sample points being left lower corners. Let R be the Riemann sum corresponding to the right lower corners. Which of the following inequalities are true: I < L I < R 0 2 2 2 Problem 2. Find the volume of the solid bounded by the surface z = 1 + ex sin y and the planes x = 1, y = 0, y = , z = 0. Problem 3. Use double integral to find the area enclosed by the curve r = 4 + 3 cos . Problem 4. Find the surface area of the surface z = xy that lies within the cylinder x2 + y 2 = 1 . Problem 5. Let D be a square lamina with vertices (0, 0), (0, 1), (1, 0), (1, 1) and density proportional to the distance to the y-axis. Find the moment of this lamina with respect to the axis with equation y = x.
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This note was uploaded on 04/06/2008 for the course MATH 32B taught by Professor Rogawski during the Spring '08 term at UCLA.
- Spring '08