2023 KSS P2 Q5

2023 KSS P2 Q5

Secondary 4
6 marks
  1. Differentiate \(\left(1-\dfrac1x\right)^5\) with respect to \(x\).[2]
  2. Hence find the exact value of \(\displaystyle\int_1^2 x^{-6}(x-1)^4\,\mathrm dx\).[4]

Solution:

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Answer:(i) \(5x^{-2}\left(1-\dfrac1x\right)^4\). (ii) \(\dfrac1{160}\).

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