Standard +0.8 This is a solid of revolution problem requiring integration by parts on x²e^(2x). While the setup is standard (V = π∫y² dx), the integration requires applying integration by parts twice, which is more demanding than typical A-level questions. The algebraic manipulation and bookkeeping across multiple steps elevates this above average difficulty, though it remains a recognizable technique-based question without requiring novel insight.
\includegraphics{figure_1}
Figure 1 shows the finite region \(R\), which is bounded by the curve \(y = xe^x\), the line \(x = 1\), the line \(x = 3\) and the \(x\)-axis.
The region \(R\) is rotated through 360 degrees about the \(x\)-axis.
Use integration by parts to find an exact value for the volume of the solid generated. [7]
\includegraphics{figure_1}
Figure 1 shows the finite region $R$, which is bounded by the curve $y = xe^x$, the line $x = 1$, the line $x = 3$ and the $x$-axis.
The region $R$ is rotated through 360 degrees about the $x$-axis.
Use integration by parts to find an exact value for the volume of the solid generated. [7]
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q7 [7]}}