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Double Integrals Reading Assignment: 5.1, 5.2 Recommended Problems: 5.1: 5, 7, 8, 11, 13; 5.2: 1, 3, 5, 7, 9, 10, 11, 13, 22, 26, 27, 28, 29 Evaluate each of the following if R [1,1] [0, 2] : 1) ( x 2) (ax by c) dA (a, b, c arbitrary constants) R 2 y3 ) dA R 3) Find the volume of the solid whose top is z xy cos( x 2 ) , whose base is the rectangle [0,1] [0, 2] and whose sides are vertical. 4) Let R be the region bounded by the y-axis and the parabola x = 4y - y2. Find the integral over R of f(x, y) = xy. 5) A certain double integral over a region R is computed as /6 cos x 0 sin x sec x dy dx . Plot the region R and calculate the value of the integral. 6) Show that if f is defined on [a, b] and g is defined on [c, d], then over the rectangle R = [a, b] [c, d], 7) Evaluate R e b d a c f ( x) g ( y) dA ( f ( x) dx)( g ( y) dy) . x y R dA where R is the interior of the triangle whose vertices are (0, 0), (1, 3) and (2, 2). 8) Write the integral obtained when you change the order of integration in 1 1 1 | y| f ( x, y ) dx dy .