The line \(y = mx\) bisects the area enclosed by the lines \(x = 0\), \(y = 0\), \(x = \frac{3}{2}\) and the curve \(y = 1 + 4x - x^2\). Then, the value of \(m\) is:
Show Hint
Instead of integrating the linear function \(y = mx\) with calculus, save valuable time by treating it as a simple right-angled triangle where \(\text{Base} = b\) and \(\text{Height} = m \cdot b\). The geometric triangle area formula gives: \(\text{Area} = \frac{1}{2} \cdot b \cdot (mb) = \frac{mb^2}{2}\).