This isn't homework to be handed in, but a worksheet to help me practice. I am having difficulty with the lecturers solutions more than anything.

I have attached a rather long image with problems and his solutions. (a) and (b) are trivial and I understand (g). But I immediately got stuck on question (c). Can someone explain what he is doing here in particular? I am familiar with integration and the formula he's using is:
\(V_{avg}=\frac{1}{T}\int_{0}^{T}{vdt}\)
Where T is meant to be the time period, however I am not sure where he's got 0.02pi from.

Any and all advice is desired for all the questions, taking into account that this is just for practice, so feel free to blurt out any alternative solutions if it is of no trouble.

Jim.

 

Do I need to clarify anything else?

 

A general sine wave is represented as sin(wt)
where w=angular frequency=2*pi*f=2*pi/T
f=frequency(in hertz)
T=time period(in second)

So now T=w/(2*pi)
In your problem(c)
w=50 rad/sec
so T=0.04 pi
But since as the solution says you integrate for only half time period so
(T/2)= .02 pi