calc question - help!!!

[chica2006]

Help:
evaluate (check by differentiating)

[integral] (t^2e-t3)

heres what I have but it's messed up:
= [integral] t^2 [integral] (e^-t3)
for e
dt/dx=f(x)=3te^-t3
du/dt=t^3/3te^-t3 = du = 3tdt
[integral] e^udu
[integral] e^udu= e^u + C
=e^-t3 + C

*** but what about t^2
do I do [integral] (t^2) = t^3/3 then tag it on to the 'e' part of the question?? Help I am so confused

 

[royhaas]

If you are trying to evaluate \(\displaystyle ]\int t^2 e^{-t^3}dt\), you don't need integration by parts. A simple substitution \(\displaystyle u=t^3\) will do, and the answer is simply \(\displaystyle - e^{-t^3}/3+C\), which you can verify by taking the derivative. You are making this a harder problem than it is; it's only an application of the chain rule.

 

[soroban]

Hello, chica2006!

Evaluate (check by differentiating): \(\displaystyle \L\:\int t^2 e^{-t^3}\)

here's what I have but it's messed up: \(\displaystyle \;\int t^2\,dt \,*\,\int e^{-t^3}\,dt\;\) . . . totally wrong!
If we could do that, Calculus II would be a one-week course!

Big hint: let \(\displaystyle u\,=\,-t^3\)