Triple Integrals in Cylindrical and Spherical Coordinates

Tutoring on Triple Integrals in Cylindrical and Spherical Coordinates

Learning Objectives:

Understand and Apply Triple Integrals using Cylindrical Coordinates.

Math Tutoring on Triple Integrals in Cylindrical and Spherical Coordinates

Triple Integrals in Cylindrical Coordinates:

In a Cylindrical Coordinate system, a point P in space represented by an ordered triple. Converting Cylindrical to Rectangular we get                         . So the Triple Integral using Cylindrical Coordinates is –

If the solid region of integration can be easily defined using cylindrical coordinates, the result is often is much easier to evaluate.

Triple Integrals in Spherical Coordinates:

In a Spherical Coordinate system of math tutoring, a point P in space is represented by an ordered triple. Converting Spherical to Rectangular we get                            .                  So the Triple Integral using Spherical Coordinates is –

Notice the extra factors of  in the triple integral when using Spherical Coordinates. The order of integration can be changed.

 

 

 

 

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Hook Questions:

1.     Define Triple Integrals using Cylindrical Coordinates.

2.     Define Triple Integrals using Spherical Coordinates.

 

 

 

 

 

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