1. Answer the questions below involving the double integral Z Z D f(x; y)dA, where D is some region in R 2 : (a) Is it true that for ANY continuous function f(x; y), Z 4 0 Z y 0 f(x; y)dxdy = Z 4 0 Z x 0 f(x; y)dydx? If true explain. If false, explain as well and give the correct equality. Hint: Determine and plot the region D for each double integral. (b) Is it true that for ANY continuous function f(x; y), Z 1 0 Z 1 x2 f(x; y)dydx = Z 1 0 Z 1 py f(x; y)dxdy? i. If true explain. If false, explain as well. ii. When f(x; y) = 1; Z Z D f(x; y)dA = Z Z D 1dA = Area of region D: Determine this area for both integrals. Hint: Determine and plot the region D for each double integral.