Double Integrals in Polar Coordinates

Tutoring on Double Integrals in Polar Coordinates

Learning Objectives:

Understand and Apply Double Integrals in Polar Coordinates.

Math Tutoring on Double Integrals in Polar Coordinates

Sometimes a Double Integral is easier to evaluate using Polar Coordinates. This is especially true if the region of integration can be easily defined using a Polar Equation.

The following formula for conversion between rectangular and polar coordinates are needed.

Double Integrals in Polar Form:

If f is continuous in a polar region given by  where .

In math tutoring, we can determine the following using Double Integrals in Polar Form:

·        The volume of a Right Circular Cylinder.

·        The volume of a Half Sphere over a circle.

·        The volume of a Drilled Sphere.

·        Volume bounded by two Paraboloids.

 

 

 

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Hook Questions:

1.     Define Double Integrals in Polar Form.

2.     State some applications of Double Integrals in Polar Form.

 

 

 

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