too easy? too boring?
Yes, post an interesting integral or a problem related to integration (like a sum, double sum, etc which can be computed applyin' integration), 'cause I want to collect problems and their solutions to make a PDF.
I'm not gonna start yet, may be in few hours, but if someone wants to start, no problem.
(I hope we can share lots of interesting integrals.)
Okay, here's my problem: Evaluate
For the inner integral, substitute After reversing integration order we have
Now the remaining challenge is to compute Expanding as a sum we get
Inside logarithm we have the Wallis Product and its limit is The rest follows.
Okay guys, but I dunno if you read well above, you need to post problem + solution. (To add those problems into a PDF.)
Here's another problem: Evaluate
Start with series expansion for and multiply by
The integral can be evaluated easily via integration by parts, this yields
By setting we have the desired answer.