Challenging +1.8 This is a Further Maths question requiring volume of revolution with a non-standard integrand involving ln x. Students must identify correct limits (1 to 3), set up π∫y² dx, expand (x-3)²ln x, and integrate term-by-term using integration by parts twice. The multi-step integration and algebraic manipulation elevate this above standard C4 volumes of revolution, though the technique itself is well-practiced in Further Maths.
\includegraphics{figure_4}
The figure shows part of the graph of \(y = (x - 3)\sqrt{\ln x}\). The portion of the graph below the x-axis is rotated by \(2\pi\) radians around the x-axis to form a solid of revolution, S.
Determine the exact volume of S. [7]
\includegraphics{figure_4}
The figure shows part of the graph of $y = (x - 3)\sqrt{\ln x}$. The portion of the graph below the x-axis is rotated by $2\pi$ radians around the x-axis to form a solid of revolution, S.
Determine the exact volume of S. [7]
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q4 [7]}}