(a) Given that \(\int_0^a e^{2x}\,dx=50\), find the exact value of \(a\).

(b) A curve is such that \(\frac{dy}{dx}=3-2\cos5x\). The curve passes through \(\left(\frac{\pi}{5},\frac{8\pi}{5}\right)\).

(i) Find the equation of the curve.

(ii) Find \(\int y\,dx\) and hence evaluate \(\int_{\pi/2}^{\pi}y\,dx\).