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2024 MI H1 Q4

2024 MI H1 Q4

7 marks
  1. Find \(\displaystyle\int 2e^{3x} - \frac{1}{5x^2} \, \mathrm{d}x\).[3]
  2. Find the value of \(k\), where \(k > 0\), for which \(\displaystyle\int_1^k \frac{1}{2x + 1} \, \mathrm{d}x = \frac{1}{2} \ln 7\).[4]

Solution:

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Answer:(a) \(\frac23e^{3x}+\frac1{5x}+C\), \(x\ne0\). (b) \(k=10\).

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