Standard +0.3 This is a straightforward volume of revolution question requiring the standard formula V = π∫[x²+3]² dx from x=1 to x=3. It involves expanding a quadratic, integrating a polynomial, and substituting limits—all routine C4 techniques with no conceptual challenges or novel problem-solving required. Slightly easier than average due to its direct application of a standard method.
\includegraphics{figure_1}
Figure 1 shows part of a curve \(C\) with equation \(y = x^2 + 3\). The shaded region is bounded by \(C\), the \(x\)-axis and the lines \(x = 1\) and \(x = 3\). The shaded region is rotated \(360°\) about the \(x\)-axis.
Using calculus, calculate the volume of the solid generated. Give your answer as an exact multiple of \(\pi\).
[7]
\includegraphics{figure_1}
Figure 1 shows part of a curve $C$ with equation $y = x^2 + 3$. The shaded region is bounded by $C$, the $x$-axis and the lines $x = 1$ and $x = 3$. The shaded region is rotated $360°$ about the $x$-axis.
Using calculus, calculate the volume of the solid generated. Give your answer as an exact multiple of $\pi$.
[7]
\hfill \mbox{\textit{Edexcel C4 Q2 [7]}}