A curve has equation $y = \mathrm { f } ( x )$, where $$\mathrm { f } ( x ) = x ( x - p ) ( x - q ) ( r - x )$$ with $0 < p < q < r$. You are given that: $$\begin{aligned}
& \int _ { 0 } ^ { r } \mathrm { f } ( x ) \mathrm { d } x = 0 \\
& \int _ { 0 } ^ { q } \mathrm { f } ( x ) \mathrm { d } x = - 2 \\
& \int _ { p } ^ { r } \mathrm { f } ( x ) \mathrm { d } x = - 3
\end{aligned}$$ What is the total area enclosed by the curve and the $x$-axis for $0 \leq x \leq r$ ? A 0 B 1 C 4 D 5 E 6 F 10
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A curve has equation $y = \mathrm { f } ( x )$, where
$$\mathrm { f } ( x ) = x ( x - p ) ( x - q ) ( r - x )$$
with $0 < p < q < r$.
You are given that:
$$\begin{aligned}
& \int _ { 0 } ^ { r } \mathrm { f } ( x ) \mathrm { d } x = 0 \\
& \int _ { 0 } ^ { q } \mathrm { f } ( x ) \mathrm { d } x = - 2 \\
& \int _ { p } ^ { r } \mathrm { f } ( x ) \mathrm { d } x = - 3
\end{aligned}$$
What is the total area enclosed by the curve and the $x$-axis for $0 \leq x \leq r$ ?
A 0
B 1
C 4
D 5
E 6
F 10