# Integral problem w/ both limits as variable

• Feb 15th 2010, 11:31 AM
Fdoka
Integral problem w/ both limits as variable
Hey all, I'm very new to these forums. I'm not looking for the answers, but rather to figure out if the way I go about doing this problem is correct or if I am totally wrong any explanation would be very appreciated.

Question: Use the fundamental theorem of Calculus to find the derivative of the given function
$\int_{x^3}^{x} cos(t^3)dt$

What I did:
$\int_{x^3}^{x} cos(t^3)dt$ = $\int_{0}^{x} cos(t^3)dt$ - $\int_{0}^{x^3} cost(t^3)dt$ = $cos(x^3) - cos(x^9) * 3x^2$

**Ive never used LaTeX before so I hope this is the right way of showing it.
**If I messed up the whole thing or any part please give me tips on where I went wrong, thank you!

P.S - is there any online program that I could input an integral such as this so I can check myself?

Sorry for all the questions + thank you!
• Feb 15th 2010, 12:35 PM
tom@ballooncalculus
Looks good. Latex good too! Tiny typo cost(t...

I don't think that http://www.wolframalpha.com/ can do this particular task, at least, my attempt to input

differentiate int _(x^3) ^x cos(t^3) dt

caused 'server unavailable' - my syntax possibly wrong...
• Feb 15th 2010, 12:46 PM
Fdoka
Thanks for your help (Rock). Ive also tried using that web-site but it does not seem to work for me either >.<;;
• Feb 15th 2010, 12:54 PM
vince
nevermind...i just noticed you have it right...didnt even check till after i posted...lol...time to take a break. later on.