# Complicated “functional integral”

I came across the following "functional" at work:

$$\Pi [b]=\iint_0^{\lambda b(v,\lambda)} vf(v,\lambda) \; dv \; d\lambda$$

it's part of an optimization problem that tries to find $b$, subject to some constraints on $b$.

I'm not familiar with that type of integral, where the solution function is actually in one of the bounds of the integral. Is there a specific name for that type of integral? Would the calculus of variations address that type of optimization problem? Or is there a field of functional analysis (calculus?) that would address it?

Thanks!

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 Are you integrating with respect to $v$ or $\lambda$? Surely it can't be with respect to both? – Bruno Dec 1 '11 at 3:51 Yeah, I'm afraid it's with respect to both... But you are right, I need to fix the formula :-) Thanks! - the second integral is from 0 to +infinity. – Frank Dec 1 '11 at 4:04