5 The function f is defined by \(\mathrm { f } ( x ) = ( x + a ) ( x + 3 a ) ( x - b )\) where \(a\) and \(b\) are positive integers.
- On the axes in the Printed Answer Booklet, sketch the curve \(y = \mathrm { f } ( x )\).
- On your sketch show, in terms of \(a\) and \(b\), the coordinates of the points where the curve meets the axes.
It is now given that \(a = 1\) and \(b = 4\).
- Find the total area enclosed between the curve \(y = \mathrm { f } ( x )\) and the \(x\)-axis.