(1 paint) Write limits of integration for the integral fw g(w, y, Z) all": where W is the half cylinder shown. iflhe length of the cylinder is 2 and its radius is 3. Z (Note: values for all answer blanks must be supplied for ThlS problern to be able to check the answers provided.) Note: You can earn partial credit on this problem (1 point) Find the volume of the region between the graph of f(x, y) = 16 - x - y and the cyplane. volume = 30pi(1 point) Convert the integral to polar coordinates and evaluate it (use t for 0) With a = -pi/6 , b= pi/6 0 and d = sqrt(6)/cos(t) for S, dyda = Safer dr dt = 1 1/2 * 6/cos^2(t) dt b = 3 [tan(t)] 2sqrt(3)(1 point) For each of the following, set up the integral of an arbitrary function f(@, y) over the region in whichever of rectangular or polar coordinates is most appropriate. (Use t for 0 in your expressions.) (a) The region 1 0- -1 140 -1 With a = 0 b = 1 4 and d = 8 integral = fo f f(x,y) d X (b) The region (sqrt(3)2,2) -110 - -1 With a = 0 b = 4 0 and d = 4 integral = ford