Saturday, June 14, 2025

Evaluating a Double Integral over General Polar Regions of Integration

 Goal: Evaluate a double integral over a general polar of integration

To evaluate the double integral of a continuous function over polar general regions using iterated integrals, we consider the types I and II regions used previously in the calculation of double integrals over general regions in rectangular coordinates. We write polar equations as r = f(θ) rather than θ = f(r). The general polar region is defined by:

 


 
The figure above represents the general polar region between ɑ ≤θ ≤ β and h₁ (θ) ≤θ ≤ h₂(θ)

Theorem


Example


Solution



Practice



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