3.4.6. Double integral in polar coordinates

Let the domain D be regular in polar coordinates, i.e. the line φ = c , ( c - const ) intersects the boundary of the domain D no more than two times. Let the domain D be given by the inequalities β ≤ φ ≤ α , ρ ₁ ( φ ) ≤ ρ ≤ ρ ₂ ( φ ).

Then the double integral the functions f ( x, y ) , given in rectangular coordinates, can be reduced to calculating the double integral in polar coordinates:

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