Determine the rms value of a semi-circular current wave which has a maximum value of a.

The equation of a semi-circular wave (shown in figure) isx2+y2=a2  or   y2=a2−x2Irms=12a∫−a+ay2dxI2rms=12a∫−a+a(a2−x2)dx=12a∫−a+a(a2dx−x2)dx=12a|a2x−x33|−a+a=12a(a3−a33+a3−a33)=2a33Irms=2a23=0.816a