Question

Explain when it is necessary to convert a double integral from cartesian coordinates to polar coordinates.

Answer 1

Answer:

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Step-by-step explanation:

• Again, just as in section on Double Integrals over Rectangular Regions, the double integral over a polar rectangular region can be expressed as an iterated integral in polar coordinates. Hence, ∬Rf(r,θ)dA=∬Rf(r,θ)rdrdθ=∫θ=βθ=α∫r=br=af(r,θ)rdrdθ. ∬Rf(x,y)dA=∬Rf(rcosθ,rsinθ)rdrdθ.

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Answer 2

Answer:in section on Double Integrals over Rectangular Regions, the double integral over a polar rectangular region can be expressed as an iterated integral in polar coordinates. Hence, ∬Rf(r,θ)dA=∬Rf(r,θ)rdrdθ=∫θ=βθ=α∫r=br=af(r,θ)rdrdθ. ∬Rf(x,y)dA=∬Rf(rcosθ,rsinθ)rdrdθ

Step-by-step explanation: