mcint2 <- function ( f, xdom, bdom, m = 1000 )

#*****************************************************************************80
#
## mcint2() estimates an integral over a rectangle using a Monte Carlo approach.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    09 March 2020
#
#  Author:
#
#    Original R code by James Howard;
#    This version by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017
#    ISBN13: 978-1-4987-2363-3.
#
#  Input:
#
#    real F(x,y): the integrand.
#
#    real XDOM(2): the left and right limits of the rectangle.
#
#    real YDOM(2): the bottom and top limits of the rectangle.
#
#    integer M: the number of sample points to use.
#
#  Output:
#
#    real AREA: the integral estimate.
#
{
  xmin <- min ( xdom )
  xmax <- max ( xdom )
  x <- runif ( m, min = xmin, max = xmax )

  ymin <- min ( ydom )
  ymax <- max ( ydom )
  y <- runif ( m, min = ymin, max = ymax )

  z <- f ( x, y )
  area <- ( xmax - xmin ) * ( ymax - ymin ) * sum ( z ) / m

  return ( area )
}