The discussion revolves around evaluating a double integral of the function (x+2y) over a region R in the first quadrant, which is bounded by the circle defined by the equation x²+y²=9. Participants are focused on determining the appropriate limits of integration for this double integral.
The discussion is progressing with participants confirming the limits for y as 0 to sqrt(9-x²) and for x as 0 to 3. There is an acknowledgment of the need to determine the order of integration, and guidance has been provided regarding the setup of the iterated integral.
Participants are navigating the challenge of accurately defining the limits of integration without falling into the trap of misrepresenting the region as a square, which does not reflect the actual bounded area of the circle.
How would you describe the region R as a set? IOW, R = {(x, y) | <inequality involving x> and <inequality involving y>}.Math10 said:Homework Statement
Evaluate the double integral (x+2y)dA, where R is the region in the first quadrant bounded by the circle x^2+y^2=9.
Homework Equations
None.
The Attempt at a Solution
I know how to evaluate the double integral but I just don't know how to find the limits of integration. I know that the radius of the circle is 3.
That would be a square in the first quadrant.Math10 said:From 0 to 3?
Why would y be negative?Math10 said:So y=sqrt(9-x^2) and y= - sqrt(9-x^2)?
Yes. Now what are your limits for x?Math10 said:So y=0 to sqrt(9-x^2)?
You tell me ...Math10 said:dy dx?