| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | September |
| Marks | 5 |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find constant from definite integral |
| Difficulty | Moderate -0.8 This is a straightforward integration question requiring basic power rule application (rewriting 36/x² as 36x^(-2)) followed by substituting limits into the result and solving a simple linear equation for a. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial since it requires correct handling of negative powers and definite integral evaluation. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
1.
\begin{enumerate}[label=(\alph*)]
\item Find $\int \left( \frac { 36 } { x ^ { 2 } } + a x \right) \mathrm { d } x$, where $a$ is a constant.\\[0pt]
[3 marks]
\item Hence, given that $\int _ { 1 } ^ { 3 } \left( \frac { 36 } { x ^ { 2 } } + a x \right) \mathrm { d } x = 16$, find the value of the constant $a$.\\[0pt]
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q1 [5]}}