2026 GESS P1 Q7

2026 GESS P1 Q7

Secondary 4
8 marks
  1. Show that \(\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\ln x^2}{3x}\right)=\dfrac2{3x^2}-\dfrac{2\ln x}{3x^2}\).[3]
  2. Hence integrate \(\dfrac{\ln x}{x^2}\) with respect to \(x\).[3]
  3. Given that the curve \(y=f(x)\) passes through the point \((1,3)\) and is such that \(f'(x)=\dfrac{\ln x}{x^2}\), find \(f(x)\).[2]

Solution:

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Answer:(a) Shown for \(x>0\). (b) \(-\dfrac{1+\ln x}{x}+C\). (c) \(f(x)=4-\dfrac{1+\ln x}{x}\).

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