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2024 YIJC H1 Q2

2024 YIJC H1 Q2

7 marks
    1. Differentiate \(\mathrm{e}^{\mathrm{e}^x}\) with respect to \(x\).[2]
    2. Hence find \(\displaystyle\int \mathrm{e}^{\mathrm{e}^x+x+1} \, \mathrm{d}x\).[2]
  2. Find \(\displaystyle\int \left( \frac{1}{2x^2} - \sqrt{x} \right)^2 \, \mathrm{d}x\).[3]

Solution:

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Answer:

(a)(i) \(e^{e^x+x}\). (ii) \(e^{e^x+1}+C\).

(b) \(-\frac1{12x^3}+\frac2{\sqrt x}+\frac12x^2+C\), for \(x>0\).

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