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]