# evaluating an integral with two functions as limits of inegration

• November 28th 2012, 11:08 AM
kingsolomonsgrave
evaluating an integral with two functions as limits of inegration
$F(x)=\int_{x^4}^{x^3} (2t-1)^3\ dt$

how do I go about doing this given that there are two functions as the upper and lower limit (as opposed to one of them being a function and the other being a constant)

would I let one of them =u and the other =v and then try to work from there? If so how would the derivatives and anti-derivatives work?
• November 28th 2012, 12:29 PM
Plato
Re: evaluating an integral with two functions as limits of inegration
Quote:

Originally Posted by kingsolomonsgrave
$F(x)=\int_{x^4}^{x^3} (2t-1)^3\ dt$

Once and for all. If each of $f~\&~g$ is a differentiable function and $\Phi (x) = \int_{g(t)}^{f(x)} {h(t)dt}$
then $\Phi '(x) = f'(x)h(f(x)) - g'(x)h(g(x))$.