Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a specific problem that Ive generalized here for simplicity.

Let $F(x)=\int^{g(x)}_0h(x,y)dy $

Suppose $F(0)=0$ (with $g(0)>0$)

Now suppose that $h$ is increasing in $y$. Then, it follows that:

$F(x) \leq g(x) h(x,g(x)) $

Does it therefore have to be the case that $h(0,g(0)) = 0$?

share|improve this question
add comment

1 Answer 1

up vote 1 down vote accepted

Not at all. Let $g(x) = 1$ be constant and $h(x,y) = 2y - 1$. Then $h(0,g(0)) = 1$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.