(a)[4]
Use the trapezium rule with three intervals to show that the value of $\int_{1}^{4} \ln x\,dx$ comes out as approximately $\ln 12$.
(b)[2]
Use a graph of $y = \ln x$ to show that $\ln 12$ underestimates the true value of $\int_{1}^{4} \ln x\,dx$.