help evaluating an integral

sneaky · P versus NP Offline Joined: 17 Oct 2009 Posts: 43

integral sign of 0 to t

(21e^8)sin(t-s)ds

i keep getting 0 as final, but it is wrong

**Posted:** Thu Nov 19, 2009 7:36 pm

Kent Merryfield

The way I read it, you wrote $\int_0^t21e^8\sin(t-s)\,ds$

I suspect that's not what you meant, including that I suspect that's not supposed to be $e^8,$ but I'm not that good a mind reader.

Click on what I wrote (or what anyone else here writes) to see the codes needed to make it look like that; put that between dollar signs to have it show up on the forum.

**Posted:** Thu Nov 19, 2009 7:49 pm

sneaky · P versus NP Offline Joined: 17 Oct 2009 Posts: 43

i made one mistake, change the power of 8 to power of s

**Posted:** Thu Nov 19, 2009 8:11 pm

kunny

Let $t-s=u,\ \int_0^t e^t\sin (t-s)\ ds=e^s\int_0^t e^u\sin u\ du$ .

**Posted:** Thu Nov 19, 2009 8:22 pm

_________________
Today's calculation of Integral Digest

kenn4000

kunny im pretty sure you shouldnt have an s anywhere since its a dummy variable.

$\int_0^t e^s \sin (t-s)ds= e^t\int_0^t e^{s-t} \sin(t-s)ds = e^t \int_0^t e^{-w}\sin w dw$

$=\frac{e^t - (\cos t +\sin t)}{2}$ after two by parts integrals

**Posted:** Thu Nov 19, 2009 9:51 pm