2025 PHS P1 Q12

2025 PHS P1 Q12

Secondary 4
8 marks
  1. Given that \(y=3x\sqrt{7+x^3}\), show that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) can be written in the form \(\dfrac{a+bx^3}{2\sqrt{7+x^3}}\).[4]
  2. Hence or otherwise, evaluate \(\displaystyle\int_0^1\dfrac{14+5x^3}{2\sqrt{7+x^3}}\,\mathrm{d}x\), leaving your answer in surd form.[4]

Solution:

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Answer:(a) \(\dfrac{42+15x^3}{2\sqrt{7+x^3}}\). (b) \(2\sqrt2\).

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