Turn over 19 Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 6 marks) 20 7. In this question you must show all stages of your working. You must not use the integration facility on your calculator. In = t t t n∫ + 4 5 2 d         n  0 (a) Show that, for n > 1 I t n t n n I n n n = + + ( ) − − + − − 1 2 3 2 2 5 2 4 5 4 1 5 2 ( ) ( ) ( ) (5) y x O Figure 1 The curve shown in Figure 1 is defined by the parametric equations x = 1 5  t 5        y = 1 2  t 4            0  t  1 This curve is rotated through 2π radians about the x‑axis to form a hollow open shell. (b) Show that the external surface area of the shell is given by (5) 1 7 2 0 4 5 d π t t t + ∫ Using the results in parts (a) and (b) and making each step of your working clear, (c) determine the value of the external surface area of the shell, giving your answer to 3 significant figures. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________