Hi, I am having some trouble with this integral problem,
I believe it is integration by parts. I don't know the "[m@th][/m@th]" tags so if someone could point me to a link that would be great too.
Thanks,
Matt
i am really surprised by this
you manage to do $\displaystyle \int e^{-t}~dt$ but you can't do $\displaystyle \int-e^{-t}~dt$? i don't get you
Note that $\displaystyle \int-e^{-t}~dt = - \int e^{-t}~dt$ which you know how to find, because you did it already
is it the limits that are bothering you? you know how to use the fundamental theorem of calculus?
Okay, I get $\displaystyle -te^{-t}-\int_0^2-e^{-t}~dt$
And I am stuck with the new integral to the right. Yes, I do know the fundamental theorem of calculus. Could you just show me the steps to the whole problem? I really appreciate your time and help.
you're lucky i have to leave now, so i can't spend the time having you work things out
$\displaystyle \int_0^2 te^{-t}~dt = -te^{-t} - \int_0^2 -e^{-t}~dt$
$\displaystyle = -te^{-t} + \int_0^2 e^{-t}~dt$
$\displaystyle = -te^{-t} - e^{-t} \bigg|_0^2$
$\displaystyle = -(t + 1)e^{-t} \bigg|_0^2$
$\displaystyle = -(2 + 1)e^{-2} - [-(0 + 1)e^0]$ .............by the fundamental theorem of calculus
$\displaystyle = -3e^{-2} + 1$