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integration assignment 1 - Due 7th September Name 1 Using...

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Due: 7 th September Name: ______________________________ 1. Using the substitution u = 2 1 x + 1, or otherwise, find the integral + 1 2 1 x x d x . Working: Answer: ………………………………………….. (Total 4 marks) 2. Find the real number k > 1 for which + k x 1 2 1 1 d x = 2 3 . Working: Answer: .... …………………………………… .......... (Total 4 marks) 1
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3. Let f (t) = . d ) ( Find . 2 1 1 3 5 3 1 t t f t t Working: Answer: .......................................................................... (Total 3 marks) 4. Using the substitution y = 2 – x , or otherwise, find 2 2 x x d x. Working: Answer : ......................................................................... (Total 6 marks) 2
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5. (a) Find + m x x 0 3 2 d , giving your answer in terms of m . (b) Given that + m x x 0 3 2 d = 1, calculate the value of m . Working: Answers : (a) .................................................................. (b) .................................................................. (Total 6 marks) 6. The function f ′ is given by f ′( x ) = 2sin - 2 5 π x .
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