Piecewise Integral

$B(t)$ and $H(t)$ are time-varying quantities which are related to each other in the piecewise manner illustrated above. The transition point from one curve to another is $(B,H) = (1,1)$ .

Additionally, the following pieces of information are known:

$\large {\int_{t=0}^{t = \pi} H(t) \, dt = 4} \hspace{2cm} B(t) = \alpha \, \sin(t)$

If $\alpha$ is a positive real number, determine the value of $\alpha$ to 3 decimal places.