AS June 2024 Paper 1 Q2

2 The function f is defined by

\[\mathrm{f}(x) = 2x + 3 \qquad 0 \leqslant x \leqslant 5\]

The region \(R\) is enclosed by \(y = \mathrm{f}(x)\), \(x = 5\), the \(x\)-axis and the \(y\)-axis.

The region \(R\) is rotated through \(2\pi\) radians about the \(x\)-axis.

Give an expression for the volume of the solid formed.

Tick (✓) one box. [1 mark]

• \(\pi\displaystyle\int_0^5 (2x + 3)\,\mathrm{d}x\)
• \(\pi\displaystyle\int_0^5 (2x + 3)^2\,\mathrm{d}x\)
• \(2\pi\displaystyle\int_0^5 (2x + 3)\,\mathrm{d}x\)
• \(2\pi\displaystyle\int_0^5 (2x + 3)^2\,\mathrm{d}x\)