#lang racket

(define (monte-carlo trials experiment)
  (define (iter trials-remaining trials-passed)
    (cond 
      ((= trials-remaining 0) (/ trials-passed trials))
      ((experiment) (iter (- trials-remaining 1) (+ trials-passed 1)))
      (else (iter (- trials-remaining 1) trials-passed))))
  (iter trials 0))

(define (square x)
  (* x x))

(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random range))))

(define (P x y)
  (define (inside-circle? radius centre-x centre-y)
    (<= (+ (square (- x centre-x))
           (square (- y centre-y)))
        (square radius)))
  (inside-circle? 1.0 0 0))

(define (estimate-integral P x1 x2 y1 y2 trials)
  (define (in-region)
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (P x y)))
  (define (rectangle-area x1 x2 y1 y2)
    (* (- x2 x1) (- y2 y1)))
  
  (* (monte-carlo trials in-region) 
     (rectangle-area x1 x2 y1 y2)))