Double Integral

iocal

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How can I evaluate the following double integral:

x<u,y<v,x2+y2<1dxdy\displaystyle \displaystyle \iint\limits_{\substack{x<u,y<v, \\ x^2+y^2<1}} dxdy


Thank you.
 
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How can I evaluate the following double integral:

x<u,y<v,x2+y2<1dxdy\displaystyle \displaystyle \iint\limits_{\substack{x<u,y<v, \\ x^2+y^2<1}} dxdy


Thank you.

When did latex make it into thread titles?

Here is how I interpret your given integral:

1min{u,1}1x2min{v,1x2}dydx\displaystyle \displaystyle \int_{-1}^{\text{min}\{u, 1\}} \int_{-\sqrt{1-x^2}}^{\text{min}\{v,\sqrt{1-x^2}\}} dy dx

Lower bound being the bottom of a disk, with x being at most some constant u, and y at most some constant v. But you need to be careful here, as u and v might lie outside of the disk.
 
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