Standard +0.3 This is a straightforward volume of revolution question requiring the standard formula V = π∫y² dx. The integration involves a simple algebraic manipulation (the square root squares away nicely) leading to a standard form that integrates to arctan. While it's from Further Maths, the technique is routine and the algebra is clean, making it slightly easier than an average A-level question.
2 In this question you must show detailed reasoning.
The finite region \(R\) is enclosed by the curve with equation \(y = \frac { 8 } { \sqrt { 16 + x ^ { 2 } } }\), the \(x\)-axis and the lines \(x = 0\) and \(x = 4\). Region \(R\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis. Find the exact value of the volume generated. [4]
2 In this question you must show detailed reasoning.
The finite region $R$ is enclosed by the curve with equation $y = \frac { 8 } { \sqrt { 16 + x ^ { 2 } } }$, the $x$-axis and the lines $x = 0$ and $x = 4$. Region $R$ is rotated through $360 ^ { \circ }$ about the $x$-axis. Find the exact value of the volume generated. [4]
\hfill \mbox{\textit{OCR Further Pure Core 2 2017 Q2 [4]}}