Evaluate Contour Integral

Question

I have provided my solution below, a confirmation on my solution would be appreciated, thanks in advance.

Answer 1

Your parameterization is wrong. You need $z(t)=e^{it}$, $0\le t\le\pi$. Under this parameterization, $y=\sin t$ and the integral becomes $$\int_C5y\,\mathrm dz=5\int_0^\pi\sin t\cdot ie^{it}\,\mathrm dt=5i\int_0^\pi\cos t\sin t+i\sin^2t\,\mathrm dt\\ =\tfrac{5}2\int_0^\pi i\sin2t-1+\cos2t\,\mathrm dt=-\frac{5\pi}2.$$