# Thread: [SOLVED] Application of calculus for finding expression?

1. ## [SOLVED] Application of calculus for finding expression?

Power transmitted along the string by a sinewave is given by P = μ*ω^2*A^2*v*cos^2 (ωt - kx). Find expression for average power over t = 0 to t = T.
[ω = 2π/T]

How to do it? Please explain all the steps.

2. Originally Posted by fardeen_gen
Power transmitted along the string by a sinewave is given by P = μ*ω^2*A^2*v*cos^2 (ωt - kx). Find expression for average power over t = 0 to t = T.
[ω = 2π/T]

How to do it? Please explain all the steps.

Is everything assumed to be a constant that isn't t? In other words what is the variable as to which we are supposed to be differentiating in respect to?

3. I dont know for sure myself. But since the question asks for expression over t= 0 and t = T, i think w.r.t t. I think we have to assume the others to be a constant.

4. Originally Posted by fardeen_gen
I dont know for sure myself. But since the question asks for expression over t= 0 and t = T, i think w.r.t t. I think we have to assume the others to be a constant.
I assmume it wants this

Let $P\left(\mu,\omega,A,v,t,k,x\right)$ represent that ugly thing, then the average on $t=0\to{t=T}$ would be

$P\left(\mu,\omega,A,v,t,k,x\right)_{\text{average} }=\frac{1}{T}\int_0^{T}P\left(\mu,\omega,A,v,t,k,x \right)dt$