Question: Question 1 Using various techniques of integration: (a) Evaluate J 1 1 + 2ex - e-x dx . (10 marks) (b) Determine the exact value

Question 1 Using various techniques of integration: (a) Evaluate J 1

Question 1 Using various techniques of integration: (a) Evaluate J 1 1 + 2ex - e-x dx . (10 marks) (b) Determine the exact value of Sex cos 2x dx . (10 marks) (c) Evaluate dx . V8x - x2- 7 (10 marks) Question 2 (a) Solve d tan-1 x c Jx2 sint dt , where x > 0, simplifying your answer as much as possible. (8 marks) (b) Determine the derivative of f (x) = In x-+1 e 2X

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