Re: Evaluating an intergal

Re: Evaluating an intergal

Whether "T" is a constant or not since it is an upper limit on the integral it has to be treated as one.

So the integral is $\displaystyle Te^{-rT}\int_0^T dt- e^{-rt}\int_0^T tdt$. I get the same thing you do. Perhaps the equation is not saying that the integral on the left gives the result on the right, but that the integral on the left is, for some other reason, equal to the right side? That is, that $\displaystyle \frac{T^2e^{-rT}}{2}= \frac{rT- e^{-rT}- 1}{r^2}$? That doesn't seem quite right but it is the only way I can make sense of it. Could you give more information about what you were reading?