13.
\includegraphics[max width=\textwidth, alt={}, center]{63d85737-99d4-4916-a479-fe44f77b1505-25_679_1043_413_607} Figure 5 shows a sketch of part of the curve with equation \(y = \frac { 6 x } { \sqrt { 3 x + 1 } } , \quad x \geq 0\)
The finite region \(\mathbf { R }\), shown shaded in figure 5 is bounded by the curve, the \(x\)-axis and the lines \(x = 2\) and \(x = 5\). Use the substitution \(u = 3 x + 1\) to find the exact area of \(\mathbf { R }\).
(Total for Question 13 is 7 marks)