Edexcel C2 — Question 7

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
TopicArea Under & Between Curves

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{da9672c1-d1d8-4c2f-89ef-2055da37f720-4_565_814_251_495} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows part of the curve \(y = \mathrm { f } ( x )\) where $$\mathrm { f } ( x ) = \frac { 1 - 8 x ^ { 3 } } { x ^ { 2 } } , \quad x \neq 0 .$$
  1. Solve the equation \(\mathrm { f } ( x ) = 0\).
  2. Find \(\int \mathrm { f } ( x ) \mathrm { d } x\).
  3. Find the area of the shaded region bounded by the curve \(y = \mathrm { f } ( x )\), the \(x\)-axis and the line \(x = 2\).