Thread:HMcCoy/@comment-28838092-20150830205938/@comment-12.218.41.6-20150831144017

Anthony Jacquez wrote: Hello HMcCoy,

I was curious about a property relating to calculus. Why does subtracting the upper bound by the lower bound of a definite integral give you it's area? It's just strange to me considering the different types of graphs you can have like a negative parabola vs a positive parabola.

Example: $$\int_a^bf(x)dx = F(b) - F(a) = Area$$

$$$ This is actually really subtle and super cool. Recall the Mean Value Theorem, which states $$\frac{f(b)-f(a)}{b-a}=f'(c) for some c\in(a,b)$$. Now, if you multiply both sides by $$b-a$$ and recognize that in limit the Riemann sum definition of the integral moves towards intervals that have "zero" length (let b->a) you end up with $$f(b)-f(a)=f'(c)$$. Now simply replace f' with f, and f with F, and you have the FTC part II! The Mean Value Theorem (MVT) is the Most Valuable Theorem (MVT) in math!

Also, can you revert TibetPrime's action on my personal user rights:

"23:36, August 28, 2015 TibetPrime (wall | contribs) changed group membership for User:Anthony Jacquez from rollback, moderator and poweruser to poweruser"

He never gave a reason for the action, so I don't believe the action can be valid.

$$$ The action was justified, you had stated that you would be out for a long while due to not having internet. Our policy says we "may" remove after a calendar month, which we did. However, at the end of next month assuming all goes smoothly I cannot imagine a reason that we would not be able to reinstate those rights. You were a fine contributor before, we just need to make sure it is still the AJ we know and love and not a possible hacker or something like that. We have had some serious issues the last while with a (formerly) strong contributor.

Thanks,

Anthony Jacquez

Please read my comments prefaced by $$$ in the text above. Regarding Cyan Wind, again using the word "may," we have not removed his rights because if and when he comes back we hope he will be able to dive into things right away. He knows coding much better than myself, for example. The admin team decided there was not a good reason to remove his rights, but we did remove his link from the menu.

I apologize for any errors, I am at school right now and don't have the time to proofread immediately.

Take care!