Finding Work from the Derivative of Power

1. Oct 6, 2011

Calam1tous

1. The problem statement, all variables and given/known data

A machine delivers power at a decreasing rate P = P(o)*t(o)^2 / (t + t(o))^2 , where P(o) and t(o) are constants. The machine starts at t = 0 and runs forever.

Find the amount of total work.

2. Relevant equations

P = w / t
W = f * d

P = P(o)*t(o)^2 / (t + t(o))^2

3. The attempt at a solution

I'm not really sure what to do here. My guess is that it is an improper (infinite) integral problem, but I'm just not sure how to really start. I tried to separate P(o) and t(o) from the equation since they are constants, but I couldn't get it work out.

Can anyone point me in the right direction?

2. Oct 6, 2011

Staff: Mentor

If you integrate power (Watts = Joules/sec) over time you will get Joules, which equates to the energy delivered. i.e., work. So do the integration