Answer Happy

unit circle. 3. Provide detailed sketches to support your work. (a) Let I = SOL" 2xy dudy. (1) Evaluate I. (11) Find and sketch the planar region R such that I = SIx2wydA. (b) Evaluate SpaydA where D is the region in the first quadrant bounded by the x-axis, the line y = 1, and the (c) Evaluate S. Selv dydt. (Hint: el/, as a function of t, has no known antiderivative in closed form; therefore, this iterated integral cannot be evaluated directly. You need to resort to some other means.) 4. Do two of the following three problems; do all for bonus. Provide detailed sketches to support your work. (a) Evaluate SSJ, edV, where E is the solid region bounded by the surfaces z = } (x2 + y2) and 2 = 2. (b) Evaluate Ilg xdV, where E = {(x,,z) |* 20, +2 + y2 < 4,05 : Sy}. (C) Let f(x,y) = y/(x2 + y2). Evaluate II, fdA where D is the upper half of the disc of radius 1 centered at (1,0). (Use polar coordinates.)