2 The function f is defined by $$f ( x ) = 2 x + 3 \quad 0 \leq x \leq 5$$ 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.
\(\pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) d x\)
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\(\pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) ^ { 2 } \mathrm {~d} x\)
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-02_115_108_1699_1000}
\(2 \pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) d x\) □
\(2 \pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) ^ { 2 } \mathrm {~d} x\) □