Question: 9. Let f(x) be a continuous function defined on the interval [0,a], where a is a positive constant. (a) (i) Prove fo f(x)dx = =

9. Let f(x) be a continuous function defined on the interval [0,a], where a is a positive constant. (a) (i) Prove fo f(x)dx = = ] [f(x)+ f(a-x)]dx. (3 marks) (ii) Let g(x) = xsinel. Is g(x) an odd function or an even function? Explain your answer. (2 marks) 1 24 (b) Using (a), evaluate 4 In(1 + tanx)dx . (4 marks) 2x (c) Using (b), evaluate dx . (5 marks) cos 2x + sin 2x + 1 (d) Using the above results, evaluate 5 7 77 - 2x+ X- (cos2x + sin 2x - 1 )sine 8 (5 marks) 8 dx . cos 2x + sin 2x -1

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