2026 CSS P1 Q12

2026 CSS P1 Q12

Secondary 4
10 marks
  1. Differentiate \(x\cos x\) with respect to \(x\).[2]
  2. Hence find \(\int(x\sin x)\,\mathrm{d}x\).[2]
  3. Differentiate \(x^2\sin x\) with respect to \(x\) and hence, using the results in (b) and (c), find \(\int(x^2\cos x)\,\mathrm{d}x\).[6]

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Answer:(a) \(\cos x-x\sin x\). (b) \(\sin x-x\cos x+C\). (c) Derivative \(2x\sin x+x^2\cos x\); integral \(x^2\sin x+2x\cos x-2\sin x+C\).

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