Uses of Rectangular, Cylindrical and Spherical Coordinates

 

 

In a Nut Shell:  Three options are available in the evaluation of double and

triple integrals.    The table below lists these options.

 

Switching from one set of coordinates to another

Changing the order of integration

Changing the variables of integration

 

This section focuses on uses of rectangular, cylindrical, and spherical coordinates in the

evaluation of double and triple integrals.  (The first option)

 

 

 

 

Rectangular Coordinates of a point, P,  in space are:    (x,  y,  z)  as shown below    

                     

 

Cylindrical Coordinates of a point, P,  in space are:   ( r ,  θ,   z  )

 

where   θ  =  angle between the  x-axis and the radius, r,  in the x-y plane as shown below

                       

 

So the rectangular coordinates (x, y, z) of P in cylindrical coordinates are:

 

                  x = r cos θ,     y = r sin θ,     z = a

 

Click here to continue with spherical coordinates.

 



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