mathematics is more beautiful when you are not studying for exam but learning for fun.

Who the hell figured this out orginally?!? Genius.

Just finished Calc I and watched this video for fun but just wanted to say I loved the clarity of her explanation!

I didn't expect a simple easy evaluation within just three minutes

The last time I solved a double integer was in 2018. This woman literally saved my life right now. That's exactly the integer I wanted to solve but couldn't remember how to. Thank you!

I swear to jeebus this is easier to understand than transformations. Amazing how it just takes a small change in perspective to make this problem easier!

Her ability to explain never ceases to amaze me. Just legendary!

She's my favourite person in the world at the moment:D

6:58 was awesome. I never thought like that

This one is very important for physics (statistics). 90% you have to solve it in a project. Nice method.

This example really blows my mind. It surprised me that adding another variable made the problem solvable in the end. Also, the explanation was very clear!

I love these MIT videos... really helps remember some of these tougher concepts.

Thank you so much, and the subtitles were so useful, because my listening is not so good at english.

I'm glad I'm revisiting my math. It's fun and almost recreational now, even though in college it felt like running a race.

Did this exercice back when I was 18, there was 1 hint which was « First show that I = sqrt (Integral from -oo to +oo of exp(-x^2-y^2)dxdy) »
Then I must say the change of variables x=r cos(t) y=r sin(t) is rather obvious.

8:16 that's the most perfect pi created by a human ever.

Thank u ma'am, came here after watching a lot of videos, but this one was really awesone enough to make a viewer complement this to u💙💙

Thank you! Great lecture on integration. I think its integrated to your viewer's minds very well. :-)

Ah, this was beautiful.  Can you imagine the joy of whoever first thought to do this?

I really enjoy Christine Breiner's lectures - they are always the epitome of clarity.