Double Integral bounded by Circle?

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SUMMARY

The discussion focuses on calculating a double integral of the function (2x - y) over a circular region defined by a radius of 2, centered at the origin. Participants emphasize the importance of determining the correct limits for integration in Cartesian coordinates, specifically noting that x ranges from -2 to 2. To find the corresponding y-values for each x, users are advised to derive the equation of the circle and solve for y, yielding two values that represent the upper and lower bounds for y.

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  • Understanding of double integrals in calculus
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  • Knowledge of the equation of a circle
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Double Integral bounded by Circle?

Double integral of (2x-y)dA bounded by circle of radius 2, centered at origin

I just need to figure out the limits for my integrals... I am basically lost, can someone show me how to break this up. I tried doing what I did with the previous triangle bound one (breaking it into 2) and that didn't work
 
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Start with the equation of the circle.
 


Are you to do this in Cartesian coordinates? The circle cuts the x-axis at -2 and 2 so x must range from -2 to 2. As SammyS suggested, write the equation of circle. The solve for y. You should get two values for y, corresponding to the lowest and highest values y can take on for a given x.
 

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