| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Topic | Areas by integration |
| Type | Area under polynomial curve |
| Difficulty | Standard +0.3 This is a straightforward integration problem requiring finding roots of a quartic (which factors nicely as a difference of squares), then applying the definite integral formula. The algebraic manipulation is routine and the integration of (2x-5)^4 is a standard chain rule application, making it slightly easier than average. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals |
The diagram below represents the graph of the function $y = (2x - 5)^4 - 1$
\includegraphics{figure_7}
\begin{enumerate}[label=(\alph*)]
\item Find the intersections of this graph with the $x$ axis. [1]
\item Hence find the exact value of the area bounded by the curve and the $x$ axis. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2021 Q7 [5]}}