page 09 MARKS 16. (a) Use integration by parts to find the exact value of ( ) 1 2 4 0 2 1 x x x e dx − + ∫ . (b) A solid is formed by rotating the curve with equation ( ) 2 4 1 x y x e = − between x = 0 and x = 1 through 2π radians about the x-axis. Find the exact value of the volume of this solid. 17. The first three terms of a sequence are given by (a) When x = 11, show that the first three terms form the start of a geometric sequence, and state the value of the common ratio. (b) Given that the entire sequence is geometric for x = 11 (i) state why the associated series has a sum to infinity (ii) calculate this sum to infinity. (c) There is a second value for x that also gives a geometric sequence. For this second sequence (i) show that (ii) find the first three terms (iii) state the value of S2n and justify your answer. [Turn over for next question 5 3 2 1 2 2 2 1