Question 3 |25%| Solve the following denite double integrals: 1 2x (a) I I (437V; + x)dydx 0 I} 2 2y 2 (b) I I e" dxdy o 0 Use double integration to calculate the area of the region bounded by the given linesfcurves: (c) y=x2. y=8-x2 (d) y=2x, y=3x, y=0 (d) y = x2. x = 3'2 Question 4 |20%| Consider the function r = 1 + cos 9 under the polar coordinate system. a) Sketch the function r = 1 + cos 6 for 9 changes from 0 to 21:. b) Find the area of the region defined by a circle 1' = 1 after cutting by the mction r = 1 + cos 6