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Sed (CoderLovesEggs) Paper 1 with Solutions · Q10

Paper 1CalculusTrigonometryGeometry

You are given that

∫0πsin⁡5xdx=1615.\int_0^\pi\sin^5x\dd x=\frac{16}{15}.

Define the total area bounded between the curves

{y=xy=2sin⁡5x+x\begin{cases}y=x\\y=2\sin^5x+x\end{cases}

for 0≤x≤a0\le x\le a as F(a)F(a).

It follows that F(a)=16F(a)=16 when aa equals:

A16π15\dfrac{16\pi}{15};
B8π15\dfrac{8\pi}{15};
C8π8\pi;
D16π16\pi;
E15π15\pi;
F15π2\dfrac{15\pi}2;
Gnone of the values above.

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