Double integration using polar coordinates

[tigrisdea]

Ok, got a few small problems. Just gaps in my knowledge I suppose, wonder if anyone can help.

A bit stuck on how to work out the limits for theta. Everything else is fine, it's just that. I know if it says in the first quadrant that it's pi/2 and 0 but that's a really basic one, everything above that, no clue.

Beta function formula for anything that isn't from 0 to pi/2 :( I don't understand what number you multiply it by. Normal beta function is fine, just that.

Think that's it for now. Help would be greatly appreciated :)

 

[mathwonk]

it sounds like you are trying to memorize a formula for every situation, always useless.

try picturing what the polkar coord map does to a rectangle 0 < r < A, 0 < theta < B, when mapping it to the x,y plane by sending (r,theta) to (rcostheta, rsintheta).

 

[tigrisdea]

Uh, I'm not sure what you mean. Could you be a bit more explicit? Just so you know, I'm not taking maths any further, so I am really just trying to memorise things so I can pass the exam

 

[PowerIso]

I think what mathwonk is saying is that you should draw a picture of what is happening and realize where the bounds occur. Simply memorizing situations will illy prepare you for anything. There is not really a set pattern you follow to find the bounds, even your first quadran = pi/2 can be wrong if given the right problem.

Even if you do not plan to take more mathematics, you shouldn't plan to stop thinking critically.