Multivariable Calculus 2.3.1 - Double Integral in Polar Coordinates

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The Tutor Wizard discusses double integral in polar coordinates.
6:44 - example 1
12:35 - example 2
18:29 - example 3
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I am curious as to why we cannot make our interval for theta from 0 to 2pi? I tried this and seem to get the wrong answer.

michaelkuby