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Say I have a bi-variate distribution with a PDF $f(x,y)$ and I have a threshold defined by $y=\sqrt{c - x^2}$

I want to find the area under the curve for that threshold.

So for example if I had a distribution with single variable defined by $f(x)$ and threshold $x=t$

I would just calculate:


but I'm not sure how to put in the limits in the bi-variate case.

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It is the same. The details will depend on the function $f$, but in principle it is the double integral of $f$ over the region $y\ge \sqrt{c-x^2}$. –  André Nicolas Nov 23 '12 at 19:00
In this case geometrically it is "volume," not area, or more precisely it is probability. And I just noticed the cdf in the title. If that is what you are looking for, you want the probability that $X\le s$ and $Y\le t$. For detail, one would have to know the actual problem. –  André Nicolas Nov 23 '12 at 19:26

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