How Is Average DC Output Calculated for a Half-Wave Rectified Sine Wave?

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SUMMARY

The average DC output for a half-wave rectified sine wave is calculated using calculus integrals to evaluate the area under the voltage versus angular frequency (wt) curve over a complete cycle. The average value of the voltage is determined by dividing this area by the baseline. The voltage during the first half of the cycle is represented as V = A*sin(2πft), while the second half is zero. Frequency considerations may not be necessary for the final calculation, as they tend to cancel out.

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  • Calculus, specifically integral calculus
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  • Knowledge of half-wave rectification
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Using calculus integrals, evaluate the average dc output of a complete cycle of a half-wave rectified sine wave. Express the average value of the voltage as the area under the voltage vs wt curve, divided by the baseline.

I am completely confused. Should I be using a frequency forumula like:
1/pie (integral of) F(theta) sin [(n)(theta)] d(theta)
 
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Wouldn't the voltage be V = A*sin(2πft) for the first half period, and zero for the second half? Maybe it isn't necessary to use frequency at all since the frequency should cancel out in the end, but kind of nice to show that.
 

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