Matrix Integration

As with taking the derivative of a matrix, to integrate a matrix we simply take the integral of each individual component of the matrix;

we integrate ;

as an indefinite integral:

or as a definite integral

Example 1

cary out an indefinite integration of ;

+ C       (where C is a 3 x 3 constant matrix)

Example 2

The same principle can be applied to multiple definite integrals:

We evaluate:

This integral can be rewritten as:

Evaluating the inner integrals of each element over x with y as constant yields:

Note: select for trigonometric integrations.

Finally, we evaluate the outer integral over y and holding x as constant for each element which yields:

f