sorry, still not following you.
If we integrate by parts we have
Mn =2A \int_0^\infty x^{n+1}e^{-Ax^2}
\int_0^\infty u\frac{dv}{dx} dx=uv-\int_0^\infty v\frac{du}{dx} dx
where
u=x^{n+1} \ \ \ \ \ \frac{du}{dx}=(n+1)x^n
and
\frac{dv}{dx}=e^{-Ax^2} \ \ \ \ \ v=...
when you calculate the Moment of the following equation
p(x)=\left\{\begin{array}{cc}2Axe^{-Ax^2},&\mbox{ if }
x\geq 0\\0, & \mbox{ if } x<0\end{array}\right.
We get
Mn =2A \int_0^\infty x^{n+1}e^{-Ax^2}
solving it by parts I am getting...
I have this equation
\int_t^T n(s) (1- e^{-c (T-s)}) ds = c F(T)
and I need to differentiate both sides with respect to T
\frac{\partial }{\partial T}
to get the following result
\int_t^T n(s) ( e^{-c (T-s)}) ds = \frac{\partial F(T)}{\partial T}
How was it...