TMUA 2018 · Paper 1 · Question 12

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

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

with $0 < p < q < r$ .

You are given that:

\int_{0}^{r} f (x) d x = 0

\int_{0}^{q} f (x) d x = - 2

\int_{p}^{r} f (x) d x = - 3

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