The graph of a function h passes through the point \(\left( {\frac{\pi }{{12}}, 5} \right)\).

Given that \(h'(x) = 4\cos 2x\), find \(h(x)\).

evidence of anti-differentiation     (M1)

eg     \(\int {h'(x), \int {4\cos 2x{\text{d}}x} } \)

correct integration     (A2)

eg     \(h(x) = 2\sin 2x + c, \frac{{4\sin 2x}}{2}\)

attempt to substitute \(\left( {\frac{\pi }{{12}},5} \right)\) into their equation     (M1)

eg     \(2\sin \left( {2 \times \frac{\pi }{{12}}} \right) + c = 5,{\text{ }}2\sin \left( {\frac{\pi }{6}} \right) = 5\)

correct working     (A1)

eg     \(2\left( {\frac{1}{2}} \right) + c = 5,{\text{ }}c = 4\)

\(h(x) = 2\sin 2x + 4\)     A1     N5

[6 marks]