# Integration over region given by inequality [duplicate]

Sometimes we need to integrate over some bounded region given by inequality/inequalities. Consider the following simplest example of area of an ellipse (LaTeX code):

$\int_S dx dy$, where $S = \{ x^2/a^2 + y^2/b^2 \leq 1\}$.

Is it possible to do this directly in Mathematica? If possible, how to do it?

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Welcome to Mathematica.SE!. Please, post the Mathematica code you tried. –  belisarius Feb 10 '13 at 21:52
Check the > Scope > Integrals over Regions part of the Integrate documentation for some examples –  ssch Feb 10 '13 at 21:56
–  Sjoerd C. de Vries Feb 10 '13 at 22:18
@ssch Oh, I didn't realize there is a tutorial on this topic. I only searched the examples in vain. Thanks. –  KevinSayHi Feb 10 '13 at 22:30
I think this question puts the issue more clearly and concisely than the referenced question that it allegedly duplicates. –  m_goldberg Feb 11 '13 at 0:51