After spending some time setting up and evaluating triple integrals in cylindrical coordinates, we are going to work with triple integrals in spherical coordinates. Before doing this, let's get an overview of spherical coordinates
Overview of spherical coordinates
In a three-dimensional system of coordinates, a point P (x, y, z) is defined by:
ρ : the distance from the origin to the point P
θ: the angle from the positive direction of the x-axis as in the cylindrical coordinates system
ѱ: the angle from the positive z axis and the line OP.
Relationships between rectangular coordinates and spherical coordinates
Other important relationships for conversion
The following figures show a few regions that are useful to express in spherical coordinates
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