Question

Find the exact value of the area under one arch of the curve y(t) = V_0sin(wt). Assume V_0 and w are positive constants.

Answer 1

What problem are you having with that?

Answer 2

how to find the area of one arch of the curve

Answer 3

Integrate from t=0 to t= pi/w the function y(t) = V_0sin(wt)....the period of the sine function is 2*pi normally but the period in the case is 2pi/w, and for one arch of the curve, that is one half period, so the half period = pi/w. So then you just need to do the integral and evaluate at those limits. (0 to pi/w)......good luck.