Question 3 a). For the following problems, set up the integrals for both orders of integration (Type I and Type II). Use the more convenient order to evaluate the integral over the region R. (Give precise answers). (1). y dA, where R: trapezoid bounded by y = x, y =2x, x =1, x =2. [Verify using Mathematica] R (ii). xdA, where R: sector of a circle in the first quadrant bounded by y = v25-x, 3x-4y =0, y =0. [Verify using Mathematica] [10 + 10 = 20 marks] 2 4-x 3 b). Using polar coordinates, evaluate sin x + y dydx. [Verify using Mathematica] 0 [5 marks] c). For the following problems, sketch a graph of the region bounded by the graphs of the equations. Then use a double integral to find the area of the region. (Give precise answers). (i). Inside the cardioid r = 1+ cos @ and outside the circle r = 3 cos . [Verify using Mathematica] (ii). Inside the rose curve r = 4sin 30 and outside the circle r = 2. [Verify using Mathematica] [5 + 5 = 10 marks]