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What don't you understand?

Partial of x means y is a constant, right?

\[\int_x^y e^{-t^2}dt=-\int_y^x e^{-t^2}dt\]

By Fundamental theorem, its derivative is just replace t by x
it is = \(-e^{-x^2}\)

Ok, but why is it that partial w.r.t. x is taken after switching the limits of the integral?

because the Fundamental theorem of calculus just apply to lower limit is a constant.

Ok I understand it now, thank you for your time!

http://www.mathmistakes.info/facts/CalculusFacts/learn/doi/doi.html

Interesting read, strange that my textbook didn't mention anything of this theorem.

Actually, I learn it from this site, not from my school/books
That's why I love this site. :)

It is clear now, thanks again! ;)

What is the original problem? I don't get what you meant on the last post

oh, yeah, typo there. I see it.

So it should be \[e^{-x^{2}y^{2}}*x\]
instead of
\[e^{-y^{2}}*x\]
right?

yes, you are right. My bad.

It's ok :) What would change if the lower limit were to contain y aswell?

In that case, you have to take integral, then derivative of the result. No choice.

oh, you can break it. Give me an example, I will show you how

brb

|dw:1439212948147:dw|

Actually they have. Search.

They have all the cases, the page I gave you just the common mistake page.

I found some examples using a function of x in the upper limit. Capiche!