The equation of a curve is

\(y=x\sin x.\)

(a) Find \(\frac{dy}{dx}\).

(b) Find the equation of the tangent to the curve at \(x=\frac{\pi}{2}\) in the form \(y=mx+c\).

(c) Use your answer to part (a) to find

\(\int x\cos x\,dx.\)

(d) Evaluate

\(\int_0^{\frac{\pi}{4}}x\cos x\,dx,\)

giving your answer correct to 2 significant figures.