2026 CSS P2 Q5

2026 CSS P2 Q5

Secondary 4
8 marks
  1. Given that \(\int_0^3f(x)\,\mathrm{d}x=6\) and \(\int_3^{10}f(x)\,\mathrm{d}x=10\), evaluate
    1. \(\int_0^{10}f(x)\,\mathrm{d}x\),[1]
    2. the value of \(m\) for which \(\int_0^3[f(x)+mx^2]\,\mathrm{d}x=0\).[3]
  2. The expression \(\dfrac{4x}{2x+1}\) can be written in the form \(a+\dfrac b{2x+1}\), where \(a\) and \(b\) are integers. Find
    1. the values of \(a\) and \(b\),[2]
    2. \(\int\dfrac{4x}{2x+1}\,\mathrm{d}x\).[2]

Solution:

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Answer:(a)(i) 16. (ii) \(m=-\dfrac23\). (b)(i) \(a=2,b=-2\). (ii) \(2x-\ln|2x+1|+C\).

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