Double Integral

[iocal]

How can I evaluate the following double integral:

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


Thank you.

 

[daon2]

How can I evaluate the following double integral:

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


Thank you.

When did latex make it into thread titles?

Here is how I interpret your given integral:

\(\displaystyle \displaystyle \int_{-1}^{\text{min}\{u, 1\}} \int_{-\sqrt{1-x^2}}^{\text{min}\{v,\sqrt{1-x^2}\}} dy dx\)

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.