Standard +0.8 This is a solid of revolution problem requiring integration about the y-axis with two different functions. Students must express x in terms of y for both curves (x = √(y/2) and x = 3-y), set up the volume integral V = π∫[x₂² - x₁²]dy with correct limits, and perform algebraic manipulation before integration. The multi-step nature, need to handle two regions, and careful setup of the washer method make this moderately challenging, though the actual integration is routine once set up correctly.
Fig. 6 shows the region enclosed by part of the curve \(y = 2x^2\), the straight line \(x + y = 3\), and the \(y\)-axis. The curve and the straight line meet at \(P(1, 2)\).
\includegraphics{figure_1}
The shaded region is rotated through \(360°\) about the \(y\)-axis. Find, in terms of \(\pi\), the volume of the solid of revolution formed. [7]
Fig. 6 shows the region enclosed by part of the curve $y = 2x^2$, the straight line $x + y = 3$, and the $y$-axis. The curve and the straight line meet at $P(1, 2)$.
\includegraphics{figure_1}
The shaded region is rotated through $360°$ about the $y$-axis. Find, in terms of $\pi$, the volume of the solid of revolution formed. [7]
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q1 [7]}}