| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | February |
| Marks | 6 |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Moderate -0.3 Part (a) is a textbook integration by parts example with standard functions. Part (b) requires careful substitution work but follows a routine method once u is substituted. Both are standard techniques with straightforward execution, making this slightly easier than average but still requiring proper method application. |
| Spec | 1.08h Integration by substitution1.08i Integration by parts |
2
\begin{enumerate}[label=(\alph*)]
\item Using integration by parts, find the indefinite integral, with respect to $x$, of
$$x \cos x$$
\item Using the substitution $u ^ { 2 } = 2 x + 1$, find the indefinite integral, with respect to
$$x , \text { of } \frac { 6 x } { \sqrt { 2 x + 1 } } .$$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q2 [6]}}