INTEGRATE
Syntax
INTEGRATE ( equation|expression, symbol, symbol)
INTEGRATE ( equation, symbol;symbol, symbol;symbol)
INTEGRATE ( equation|expression, symbol, symbol, symbol)
INTEGRATE ( equation, symbol;symbol, symbol;symbol, symbol;symbol)
Implemented in iMath since version 2.2.0 or earlier.
Explanation
In the first form, create an integral for the expression or for both sides of the equation with respect to the first symbol. The third parameter is the integration constant to be used.
In the second form, create an integral for both sides of the equation with respect to the two symbols in the first list. The list in the third parameter contains the integration constants to be used. This form allows for integration to different variables on both sides of the equation.
In the third form, create an integral for the expression or for both sides of the equation with respect to the first symbol. The third parameter is the lower bound, the fourth is the upper bound. In this case of course no integration constant is required.
The fourth form allows for integration to different variables and bounds on both sides of the equation.
The integral(s) will be evaluated immediately (if possible). If you want to create an integral that should not be evaluated immediately, use INT FROM ... TO.
Example
FUNCTION { {none}, y, x}
@y@ EQDEF y = sin(x)
@int@ EQDEF INTEGRATE(@y@, x, C)
will give the result ∫y(x) dx = -cos(x) + C