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First thing that came to mind: http://www.badscience.net/ Anyone else read the book? I don't remember much of it as it was quite a few years ago, though I do remember finding it a very well written and quite often hilarious explanation of the more modern examples of "bad science" (e.g...

Ha ha ha that was a good one. Hadn't heard that, probably would've helped remembering to add the sea... Here's one: Why do mathematicians always confuse Halloween and Christmas? Because 31Oct = 25Dec. (different numerical bases). I've got to pull out the old math book go over...

Nice! Great find/post. None of the tables I found were that detailed. Do you have the direct link to that one? Several +reps and a promotion I believe are in order.

Ha ha,thanks: Yes the importance of that god damn constant is what I'd keep forgetting. Makes much more sense. I remember even back in high school doing pages and pages of indefinite integrals, everything was fine when it was marked except after every function the teacher had to write " + C "...

Any idea what was done between step 2 and 3? The integration performed. I.e: Line 2, the fraction, parameter between a and 0, integrated with respect to r. You can see line 3 their definite integral... However I've got no idea how the hell they got there. See...

Ahh... Yes now I understand, it was that last sentence I was unaware of. You're sure of that? I.e. The integral of (nothing stated) with respect to x = integral of 1 with respect to x I couldn't recall that, though as throughout maths quite often a 1 isn't specified and you can't...

What I don't get though is in the last line there isn't even a constant in the integral. The only way how I can see that last operation would work if the integral was: Integrate (1) between 2pi/5 with respect to phi. In that case you could just say 1 = phi^0 Thus integrating you would just...

Ok yeh if someone could actually explain how to integrate with respect to phi (called it theta before my bad) when it isn't a variable in the function e.g. in last line that'd be appreciated.

This is what I meant (sorry for forma/spelling etc. typing on phone): Please omit prior comment about relative sizes I forgot it was with respect to r and the a and r in te denominator would be switched to get natural log anyway however: shouldn't the definite integral in step 3 be ...

Also two things: Firstly this may be a foolish question as said due to long absence from such maths i may simply be forgetting basic things however how can one integrate with respect to theta when it isn't a variable in the actual function? Secondly why at the second step don't we just pull r...

So you don't recall the origin of this question? From where did you obtain the image?

Could you expand on the first post? I.e. specifically what topic of integration did you obtain this question from and also while I don't think I'd be able to help please let us know whether your solution was correct. Haven't studied it in some time though also don't recall ever studying compound...