Standard +0.3 This is a straightforward volumes of revolution question requiring students to apply the standard formula V = π∫y² dx, expand the squared term, and integrate. While it involves algebraic manipulation and integration of terms including x², 1/x², and 1/x⁴, these are all standard C4 techniques with no conceptual surprises. The 8 marks reflect the working required rather than exceptional difficulty, making this slightly easier than average.
\includegraphics{figure_1}
In Fig. 1, the curve \(C\) has equation \(y = f(x)\), where
$$f(x) = x + \frac{2}{x^2}, \quad x > 0.$$
The shaded region is bounded by \(C\), the \(x\)-axis and the lines with equations \(x = 1\) and \(x = 2\). The shaded region is rotated through \(2\pi\) radians about the \(x\)-axis.
Using calculus, calculate the volume of the solid generated. Give your answer in the form \(\pi(a + \ln b)\), where \(a\) and \(b\) are constants.
[8]
\includegraphics{figure_1}
In Fig. 1, the curve $C$ has equation $y = f(x)$, where
$$f(x) = x + \frac{2}{x^2}, \quad x > 0.$$
The shaded region is bounded by $C$, the $x$-axis and the lines with equations $x = 1$ and $x = 2$. The shaded region is rotated through $2\pi$ radians about the $x$-axis.
Using calculus, calculate the volume of the solid generated. Give your answer in the form $\pi(a + \ln b)$, where $a$ and $b$ are constants.
[8]
\hfill \mbox{\textit{Edexcel C4 Q10 [8]}}