Answer
$W = -82.8\ kJ$
Work Step by Step
a) The linear relationship P = aV+b results in a trapezoid shape with relevant points:
$V_1 = 0.42\ m³, P_1 = 96 kPa$
$V_2 = 0.12\ m³, P_2 = 456 kPa$
$Area = b\times \frac{h_1+h_2}{2} $
$Area = -0.3m³\times 276\ kPa$
$W = -82.8\ kJ$
b) From integration:
$W = \int PdV$
$W = \int_{0.42\ m³}^{0.12\ m³}(-1200V+600)dV $
$W = (-600V^2+600V)|_{0.42\ m³}^{0.12\ m³}$
$W = -82.8\ kJ$
