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.

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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.

MIT 18.01 Single Variable Calculus (OCW)
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how to find the area of one arch of the curve
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.

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