I need help in part a and part b

Question 3 a. Consider 1 = dr dy. i. Sketch the region of integration defined by I. ii. By reversing the order of the integration, write / as one double integral. iii. Hence show that I = 504 4225 191 - sin 65 [2+1+3=6 marks] b. Show that / 2rcosydr - 12 sinydy is independent of the path C joining (0, 0) and (1, ) . Evaluate the integral. [4 marks] c. Let 1-12 - dy dr. i. Sketch and describe the region of integration defined by J. ii. By changing to polar coordinates, evaluate J. [2+2=4 marks] d. Use cylindrical polar coordinates to evaluate / / f (x, y, 2) dV in terms of a, where f : exp (x2 + y?) ; 8 : the region bounded by the planes ? = 0andy = z, and by the cylinder r + y? = a', a > 0, = 20. [6 marks]