### defint =====================================================================

Tags
----
scripting, JS, internal, treenode, general concept

Parameters
----------
f,x,a,b[,y,c,d...]

General description
-------------------
Returns the definite integral of f with respect to x evaluated from "a" to b.
The argument list can be extended for multiple integrals (or "iterated
integrals"), for example a double integral (which can represent for
example a volume under a surface), or a triple integral, etc. For
example, defint(f,x,a,b,y,c,d).

###



#define F p2
#define X p3
#define A p4
#define B p5

Eval_defint = ->
  push(cadr(p1))
  Eval()
  p2 = pop() # p2 is F

  p1 = cddr(p1)

  # defint can handle multiple
  # integrals, so we loop over the
  # multiple integrals here
  while (iscons(p1))

    push(car(p1))
    p1 = cdr(p1)
    Eval()
    p3 = pop() # p3 is X

    push(car(p1))
    p1 = cdr(p1)
    Eval()
    p4 = pop() # p4 is A

    push(car(p1))
    p1 = cdr(p1)
    Eval()
    p5 = pop() # p5 is B

    # obtain the primitive of F against the
    # specified variable X
    # note that the primitive changes over
    # the calculation of the multiple
    # integrals.
    push(p2)
    push(p3)
    integral()
    p2 = pop() # contains the antiderivative of F

    # evaluate the integral in A
    push(p2)
    push(p3)
    push(p5)
    subst()
    Eval()

    # evaluate the integral in B
    push(p2)
    push(p3)
    push(p4)
    subst()
    Eval()

    # integral between B and A is the
    # subtraction. Note that this could
    # be a number but also a function.
    # and we might have to integrate this
    # number/function again doing the while
    # loop again if this is a multiple
    # integral.
    subtract()
    p2 = pop()

  push(p2)