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## Homework Statement

I had two small questions about the following problems.

1. Find the average and RMS values of the following waveform:

2. Show that the average and RMS values of the following sawtooth are independent of the position of the peak and are given by ##0.5## and ##0.577## of the peak value respectively.

## Homework Equations

##f_{avg} = \frac{1}{T} \int_0^T f(t) dt##

##f_{rms} = \sqrt{\frac{1}{T} \int_0^T f^2(t) dt}##

## The Attempt at a Solution

1. Looking at the function, I see it is a piecewise function with five different pieces in one period. So to compute the average/rms value would require five integrals.

Looking more closely though, I see the function is symmetric about the x-axis over one period. This implies the average value is zero right away, ##v_{avg} = 0##. Is there similar logic I can apply to find the RMS value without having to square and integrate five times? For reference I got ##v_{rms} = V##.

2. This is the same question as the first really. I'm guessing all the question wants is for me to compute ##f_{avg}## and ##f_{rms}##? What do they mean by independent of the position of the peak exactly? Am I over-thinking this one beyond the computations?