8. (**) Consider the integral I(n) = where n is a positive integer. (a) (1 mark) Evaluate I(0) = e-2: dx. (b) (7 marks) Use integration by parts to show that I(1) = 1/4 and I (2) = 1/4. (c) (7 marks) Use integration by parts to show that 2 I(n) = "I(n - 1). (d) (5 marks) Use your answers to part (a) and (c) to show that I (n) = n!/2"+1. Use this formula to confirm that your answers to part (b) are correct. Note: n!= n(n -1)(n -2) x . .. x 3 x 2x1