2024 RVHS H1 Q3
2024 RVHS H1 Q3
6 marks
- Differentiate \(\frac{\sqrt{x^3-1}}{3}\) with respect to \(x\).[1]
Hence, solve \(\displaystyle\int_3^5 \frac{2x^2}{\sqrt{x^3-1}} \, \mathrm{d}x\) exactly.[3]
- Find \(\displaystyle\int \left( e^{2x+3} + \frac{3}{5x+1} \right) \, \mathrm{d}x\).[2]
Solution:
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Answer:(a) \(\frac{x^2}{2\sqrt{x^3-1}}\); integral \(\frac43\left(\sqrt{124}-\sqrt{26}\right)\). (b) \(\frac12e^{2x+3}+\frac35\ln|5x+1|+C\), \(x\ne-\frac15\).
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