Ex-3.5

(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random range))))
(define (estimate-integral p x1 x2 y1 y2 n)
  (define (experiment)
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (p x y)))
  (* (monte-carlo n experiment) (* (- x2 x1) (- y2 y1))))

;procedure that creates a predicate to test whether
;given point lies in a circle
(define (make-in-circle-proc centreX centreY radius)
  ;for (x,y) to lie in the circle, distance
  ;between centre and (x,y) should be < radius
  (lambda (x y)
    (<= (+ (square (- centreX x))
          (square (- centreY y)))
       (square radius))))
    

;measuring PI by measuring area of unit circle  
1 ]=> (exact->inexact
 (estimate-integral
  (make-in-circle-proc 0 0 1)
  -1 1 -1 1 1000))
;Value: 3.032

1 ]=> (exact->inexact
 (estimate-integral
  (make-in-circle-proc 0 0 1)
  -1 1 -1 1 1000))
;Value: 3.008

1 ]=> (exact->inexact
 (estimate-integral
  (make-in-circle-proc 0 0 1)
  -1 1 -1 1 1000))
;Value: 2.964

1 ]=> (exact->inexact
 (estimate-integral
  (make-in-circle-proc 0 0 1)
  -1 1 -1 1 1000))
;Value: 2.952

1 ]=> (exact->inexact
 (estimate-integral
  (make-in-circle-proc 0 0 1)
  -1 1 -1 1 1000))
;Value: 3.036

1 ]=> (exact->inexact
 (estimate-integral
  (make-in-circle-proc 0 0 1)
  -1 1 -1 1 1000))
;Value: 2.948