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tmua.me Extreme Set A Paper 2 · Q12

Paper 2CalculusGeometryAlgebra

The polynomial

f(x)=x2+ax+bf(x)=x^2+ax+b

satisfies

∫01f(x) dx=0,∫01xf(x) dx=0.\int_0^1 f(x)\,\mathrm{d}x=0, \qquad \int_0^1 x f(x)\,\mathrm{d}x=0.

What is the total area between the curve y=f(x)y=f(x) and the xx-axis for 0≤x≤10\leq x\leq1?

A00
B3108\dfrac{\sqrt3}{108}
C354\dfrac{\sqrt3}{54}
D327\dfrac{\sqrt3}{27}
E2327\dfrac{2\sqrt3}{27}

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