evaluating an integral with two functions as limits of inegration

$\displaystyle 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?

Re: evaluating an integral with two functions as limits of inegration

Quote:

Originally Posted by

**kingsolomonsgrave** $\displaystyle F(x)=\int_{x^4}^{x^3} (2t-1)^3\ dt $

Once and for all. If each of $\displaystyle f~\&~g$ is a differentiable function and $\displaystyle \Phi (x) = \int_{g(t)}^{f(x)} {h(t)dt} $

then $\displaystyle \Phi '(x) = f'(x)h(f(x)) - g'(x)h(g(x))$.