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Nabla Tuition TMUA Paper 1 · Q17

Paper 1Geometry

The curve

y=x−x3y=x-x^3

lies above the xx-axis for 0<x<10<x<1.

The line x=ax=a, where 0<a<10<a<1, divides the area between the curve and the xx-axis from x=0x=0 to x=1x=1 into two equal parts.

What is the value of a2a^2?

A1−121-\frac1{\sqrt2}
B12\frac1{\sqrt2}
C2−1\sqrt2-1
D12\frac12
E2−22-\sqrt2

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