Question

Please help me get started on finding the limits of integration for the following problem:
Use a double integral in polar coordinates to find the area enclosed by the cardioid r=1-cos(theta)

Answer 1

Also, does anyone have a good resource for tutorials regarding these types of problems?

Answer 2

The integral representing the area is
\[\int\int_R dA,\]
where \(R\) is the region bounded by the cardiod and \(dA=r~dr~d\theta\) (review the derivation if you're not familiar: http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx)

\(\theta\) is bounded between \(0\) and \(2\pi\), and \(r\) is bounded between \(0\) and \(2\):
\[\int\int_R dA=\int_0^{2\pi}\int_0^2~r~dr~d\theta\]

As for your other question, the link I've provided does a great job at explaining the concept and provides a lot of worked-out examples. Highly recommended