Use the mid-ordinate rule with four strips to find an estimate for \(\int _ { 0 } ^ { 0.4 } \cos \sqrt { 3 x + 1 } \mathrm {~d} x\), giving your answer to three significant figures.
Use the substitution \(u = 3 x + 1\) to find the exact value of \(\int _ { 0 } ^ { 1 } x \sqrt { 3 x + 1 } \mathrm {~d} x\).
(6 marks)