Can you solve the following questions and provided a detailed explanation. Thank you!:)

1. Evaluate the integral [/4cos($)y3 dA Where R = {(9:44) : 0 3 cc 3 725,0 3 y S 1}. R 2. Evaluate the integral [/(sinCv2 + 342) 1) dA over D = {(5r, y) : 1 S $2 + y2 S 4}. D 3- Consider the integral / f sin(:c2y2) dA where D is the region bounded by 35' 2y2 = 0 and :2: y2 D 2y = 0. Set up but do not evaluate the integral as an iterated integral. 4. Suppose that a function z : f(:c,y) has level curves 2 = ung) = constant (2-2, -1, O, 1, 2) on the respective curves just below each of these values shown in the figure. (a) Compute the approximate average value of f in the square S : {(33, y) : 0 g :13 g 2, 0 g y g 2} using evaluation at the 4 midpoints of 4 grid cells each with Am 2 Ag 2 1. Show your midpoints and cells on a rough copy of the figure. (b) How would you improve your estimate? One or two sentence answer needed, no calculations needed. 5. Consider the integral / f \\/:r2 + Z2 dV where D is the region bounded by the paraboloid y = 53122 D and the plane y : 4. Set up but do not evaluate the integral as an iterated integral. 6. Suppose that a function 2: = at, 3;) has a small piece of its surface d3 shown shaded in the figure. As aim > 0 and dy > 0, this small piece approaches a parallelogram PQRS. You can assume that the area of PQRS is given by |a >