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Official 2018 Paper 1 · Q12

Paper 1CalculusGeometryAlgebra

A curve has equation y=f(x)y=f(x), where

f(x)=x(x−p)(x−q)(r−x)f(x)=x(x-p)(x-q)(r-x)

with 0<p<q<r0<p<q<r.

You are given that:

∫0rf(x) dx=0\int_0^r f(x)\,\dd x=0
∫0qf(x) dx=−2\int_0^q f(x)\,\dd x=-2
∫prf(x) dx=−3\int_p^r f(x)\,\dd x=-3

What is the total area enclosed by the curve and the xx-axis for 0≤x≤r0\leq x\leq r?

A00
B11
C44
D55
E66
F1010

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