RMS Value of Current
i = 4sin$\displaystyle /pi$t is 2.828A
(hint given) $\displaystyle sin^2 /theta = 1/2 (1-cos 2 /theta)$
see attached for my efforts so far.
The mean square current:
$\displaystyle p=\frac{1}{2} \int_0^2 [i(t)]^2~dt\ \ {\rm{Amps}}^2$
(the $\displaystyle 1/2$ and the limits of integration because the current is periodic with period $\displaystyle 2$), so putting in the expression for $\displaystyle i(t)$ :
$\displaystyle p=\frac{1}{2} \int_0^2 [4 \sin(\pi t)]^2~dt= 4 \int_0^2 [1- \cos(2 \pi t)]~dt=8$
hence the root mean square is $\displaystyle \sqrt{p}=2 \sqrt{2}\approx 2.828\ \ {\rm{Amps}}$.
RonL