MAC 2313 Midterm: MAC2313 S15 Test 3
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Some answers will involve square roots, fractions, , etc (1) (20 pts. ) Z 2 x 1 sin(y2 + 2y + 1) dydx by reversing the order of integration. (2) (20 pts. ) Let r be the triangular region in the (x, y)-plane with vertices (0, 0), (7, 7), and (7, 7). The density function is (x, y) = x. Find the mass, m , and the x-coordinate of the centroid, x. (3) (20 pts. ) Let t be the triangular domain in the xy-plane bounded by the three lines y = 2x, y = x, and x = 1. Let s be the part of the surface z = 3y 2x that lies above t . Using iterated double integrals, solve for the following. (a) the surface area of s (b) the volume below s and above t . (4) (20 pts. ) Let d denote the disk in the xy-plane bounded by the circle with equation y2 = x(6 x).
