.. highlightlang:: us

.. index:: integral
.. index:: Trapezoidal rule

.. _integral:

integral
========

.. us.tag  integral NOTREADYENGLISH math-lin-alg

:ref:`integral` computes an approximation of the integral via the trapezoidal 
method.

.. function::  rvIntegral = integral(rvY)
    rvIntegral = integral(rvY, bOnlyTotalValue)
    rvIntegral = integral(rvX, rvY)
    rvIntegral = integral(rvX, rvY, bOnlyTotalValue)

.. us.return

**Return Value**

If *bOnlyTotalValue* is TRUE (1) the function returns the final integral 
value (region under the graph). Otherwise *rvIntgral* is a real vector.

.. us.params

**Parameters**

.. uparam:: rvX 

   *rvX* is a vector with x coordinates.

.. uparam:: rvY

   *rvY* is a vector with y coordinates. If the function is invoked without 
   *rvX* the integral is computed with unit spacing. 

.. uparam:: bOnlyTotalValue

   If *bOnlyTotalValue* is TRUE (1), the function returns a scalar value.
   Default value is FALSE (0).

.. us.example

**Example**

::

   * rvX = 0:PI/100:PI
   * rvY = sin(X)
   * integral(rvX, rvY, 1)
        1.9998 

.. seealso::
   :ref:`overview-mathematic`

:sub:`id-675636`