help with integral from 0 to t of (x*cosx*e^(-t+x))dx

[guyga]

hey,
i need help solving this:
integral from 0 to t of (x*cosx*e^(-t+x))dx
even a hint would be great, no idea how to approach integral with 3 elements.

Thanks!

 

[Deleted member 4993]

hey,
i need help solving this:
integral from 0 to t of (x*cosx*e^(-t+x))dx
even a hint would be great, no idea how to approach integral with 3 elements.

Thanks!

\(\displaystyle \displaystyle{\int_0^tx*cos(x)*e^{x-t}dx}\)

 

[ksdhart]

For this problem, first remember the rules of exponents, and then use the integration by parts formula. Recall that e^-t+x = e^-t * e^x. Because you're integrating with respect to x, e^-t can be treated as a constant. With that out of the way, you can integrate by parts. You have two substitutions, u and v, and there's no reason why you can't have one of the variables be a substitution for two terms.

 

[guyga]

Thanks.
I didn't get to the right answer but it was pretty long so maybe i had mistake somewhere.
Understood how to do it though, thanks again

 

[aero2146]

Is the answer [tsin(t) + tcos(t) - sin(t)]/2 ?