Double integration using polar coordinates

In summary, the individual is seeking help with understanding limits for theta and the beta function formula for values outside of 0 to pi/2. They are currently trying to memorize formulas but it is not proving to be useful. The suggestion is to visualize and draw pictures to better understand the bounds instead of just memorizing specific situations. It is also advised to continue thinking critically even if not pursuing further mathematics.
  • #1
tigrisdea
2
0
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 :)
 
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  • #2
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).
 
  • #3
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
 
  • #4
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.
 

1. What is double integration using polar coordinates?

Double integration using polar coordinates is a method for finding the area under a curve in polar coordinates. It involves using two integrals, one for the radius and one for the angle, to find the area within a given region.

2. How is double integration using polar coordinates different from traditional Cartesian integration?

In traditional Cartesian integration, the area under a curve is found by integrating with respect to x or y. In double integration using polar coordinates, the area is found by integrating with respect to both the radius and angle.

3. What are the benefits of using polar coordinates for double integration?

Using polar coordinates can simplify the integration process for certain types of curves, such as circles or curves with rotational symmetry. It can also be useful when working with equations involving polar coordinates.

4. What are the steps for performing double integration using polar coordinates?

The first step is to graph the given region and determine the limits of integration for the radius and angle. Then, set up the double integral with the appropriate limits and integrate with respect to the radius and angle. Finally, solve the integral to find the area under the curve.

5. Are there any limitations to using polar coordinates for double integration?

One limitation is that not all curves can be easily expressed in polar coordinates, so this method may not be applicable in all situations. Additionally, it may be more difficult to visualize the region in polar coordinates compared to Cartesian coordinates.

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