Documentation

Compute Multiple Integrals

    Note:   Use only in the MuPAD Notebook Interface. This functionality does not run in MATLAB.

To compute multiple integrals, use nested calls to int. For example, compute the surface area and the volume of a sphere using spherical coordinates.

Compute the expression for the surface area of a sphere. The distance from the center of a sphere to the surface remains constant, r = R. The angle ϕ changes its value from 0 to π. The angle χ changes its value from 0 to 2 π:

int(int(R^2*sin(phi), phi = 0..PI), chi = 0..2*PI)

Compute the expression for the volume of a sphere. The angles accept the same values, but the distance from the center of any point inside the sphere ranges from 0 to R. To find the volume, compute the following triple integral:

int(int(int(r^2*sin(phi), r = 0..R), phi = 0..PI), chi = 0..2*PI)

Was this topic helpful?