I am a fan of the show and would love to see you cover this in a video. I teach calculus and came up with a fun problem for my students:
The answer to this integral is 5pi^2/12. The trick is to write it like this:
and then notice that this is the end result of a double integral
You can swap the order of integration and complete the square
From here, the method to use depends on the values of a and b. If |y| < 2, then the integral is an arctan. If y > 2, then we'd have to do partial fraction decomposition and integrate to logs. I'll show the first one and just state the answer for the second. Assuming the first case, we get:
Then trig sub y = 2sin(theta), the integral becomes
since arcsin(x)+arccos(x) = pi/2. The final solution is
for |a|, |b| < 2. For 2 < a < b, the answer is
by doing hyperbolic substitution on the other case. I hope this was a fun trick to see!
Just pure brilliance from you here. I have never expected something less than this from you and you have not disappointed me at all. I suppose you will keep the quality work going on. sam ovens consulting
I wanted to thank you for this great read!! I definitely enjoying every little bit of it I have you bookmarked to check out new stuff you post. sam ovens consulting
Very educating story, saved your site for hopes to read more! sam ovens consulting
Thank you very much for sharing such a useful article. Will definitely saved and revisit your site sam ovens consulting
Thank you for helping people get the information they need. Great stuff as usual. Keep up the great work!!! sam ovens consulting
I love the way you write and share your niche! Very interesting and different! Keep it coming! sam ovens consulting
Great post I would like to thank you for the efforts you have made in writing this interesting and knowledgeable article. ibuumerang
it's really cool blog. Linking is very useful thing.you have really helped ibuumerang
I have been searching to find a comfort or effective procedure to complete this process and I think this is the most suitable way to do it effectively. ibuumerang
I’m excited to uncover this page. I need to to thank you for ones time for this particularly fantastic read !! I definitely really liked every part of it and i also have you saved to fav to look at new information in your site. ibuumerang