The voltage in the electrical wiring of a house is given by  `V(t)=170sin(120pit)` Find the average voltage over the half cycle time interval `[0, 1/120]`

Expert Answers
tiburtius eNotes educator| Certified Educator

You need to calculate the following integral


which comes from formula for expected value.


`170int_0^pi x/(120pi)sin x dx/(120pi)=170/(120^2pi^2)int_0^pi x sin x dx=`

`|(u=x,dv=sin x dx),(du=dx,v=-cosx)|`

`17/(1440pi^2)(-xcosx|_0^pi+int_0^picosx dx)=17/(1440pi^2)(-xcosx+sinx)|_0^pi=`


` `The average voltage over half cycle time interval `[0,1/120]` is `17/(1440pi)`