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Compute Multiple Integrals

MuPAD® notebooks will be removed in a future release. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

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)