Question

Find the exact value of the area under one arch of the curve y(t) = V0sin(wt). Assume V0 and w are positive constants. You can use V_0 for V0. Note - V is upper case here.

Answer 1

To find the area under the curve you just integrate.

So in this case...

S (V_0*sin(w*t))dt = V_0(-cos(w*t))*w = -V_0*w*cos(w*t)

The integral from 0 to pi is

-V_0*w*cos(w*pi)) - (-V_0*w*cos(w*0)) = -V_0*w*cos(w*pi) + V_0*w = V_0*w(1 - cos(w*pi))

Good luck.