Question

Integral! (related to gamma function maybe?)
\[\int\limits_{0}^{X}\frac{\lambda^3}{2}t^2e^{-\lambda t}dt

Answer 1

Here it is: \[\int\limits_{0}^{X}\frac{\lambda^3}{2}t^2e^{-\lambda t}dt\]
I tried doing this trying to relate it to a gamma function but myupper bound is not infinity :S:
\[=\frac{\lambda^3}{2}\int\limits_{0}^{X}t^2e^{-\lambda t}dt\] \[Let : u=\lambda t =>t=u/t\]\[So: du=\lambda dt\]\[Bounds: u=0=>t=0 ; u=x=>t=x/\lambda\]
\[\frac{\lambda^2}{2}\int\limits_{0}^{X/\lambda}(\frac{u}{\lambda})^2e^{-u}du\]\[=\frac{1}{2}\int\limits_{0}^{X/\lambda}u^{3-1}e^{-u}du\]

Answer 2

why do you not just use tabular method

Answer 3

What's that?

Answer 4

it's a special type of by parts.. you can do by parts also