- #1
EngineerHead
- 21
- 0
I have a question regarding problem solving tips.
When given an iterated integral and asked to convert it to polar coordinates, how do you select the bounds of theta - do you have to understand how the graph of r operates and therefore know where the theta bounds are based on the rectangular coordinate bounds (aka completely conceptual)? Or is there a mathematical way of solving for the theta bounds?
For instance:
Set up a double integral in polar coordinates for:
f(x,y) = x+y
R: x^2 + y^2 ≤ 4
x ≥ 0
y ≥ 0
Obviously, the theta bounds are from 0->pi/2 because of the y and x bounds, but is there a mathematical procedure to arrive at this same answer? Or must you figure it out conceptually.
Thank you in advance for your help!
When given an iterated integral and asked to convert it to polar coordinates, how do you select the bounds of theta - do you have to understand how the graph of r operates and therefore know where the theta bounds are based on the rectangular coordinate bounds (aka completely conceptual)? Or is there a mathematical way of solving for the theta bounds?
For instance:
Set up a double integral in polar coordinates for:
f(x,y) = x+y
R: x^2 + y^2 ≤ 4
x ≥ 0
y ≥ 0
Obviously, the theta bounds are from 0->pi/2 because of the y and x bounds, but is there a mathematical procedure to arrive at this same answer? Or must you figure it out conceptually.
Thank you in advance for your help!
Last edited: