MATH 2043 Final: Problems.9
Document Summary
Math 2043, fall 2017: let e be the region de ned by x2/42 + y2/162 1. Compute the area of e, that is, compute. Let a and b be positive numbers, let e be the elliptical region de ned by x2/a2 + y2/b2 1. Verify using double integrals that area(e) = ab: let d be the region between the graphs of the functions g1(x) = 1 sin(x2), g2(x) = 1+sin(x2), and the lines x = 0, x = . 2: let d be the region de ned by the inequalities y x2, y (x 4)2, y x2, y (x 4)2, 0 x 4. 8: let d be the region de ned by the inequalities. 3: the region on the right is described in polar coordinates (r, ) by the inequalities. 1 r 3, 0 /3. D = {(x, y) : x = r cos , y = r sin , 1 r 3, 0 /3}
