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.)
Sorry to say, but too easy and too boring. (Read above, it's about interesting integrals.)
Yes. I hope people post problems.
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Okay, here's my problem: Evaluate
Solution:
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
Integrate
The integral can be evaluated easily via integration by parts, this yields
By setting we have the desired answer.