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.

Is it correct to state that

$\frac{d}{ds} \int_{u=0}^{u=s} f(u)du = f(s)$

if $f(u)$ is continuous?

If so, what is the relevant theorem in action? If not, what else would be needed?

share|improve this question
1  
The fundamental theorem of calculus is what you are looking for. –  Ross Millikan Oct 26 '12 at 4:18

1 Answer 1

up vote 5 down vote accepted

$\frac{d}{ds} \int_{0}^{s}f(u)du=\frac{d}{ds}(F(s)-F(0))=F'(s)=f(s)$ since $F(0)$ is a constant.

share|improve this answer

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.