calc.scm

#lang scheme
;some quick code for approximating definite integrals

;Trapezoid Rule approximation for the integral of f over range (a,b) in n divisions
(define (area-trap f a b n)
  (let ([dx (/ (- b a) n)])
    (define (iter x list)
      (cond ((= x b)
             (iter (- x dx) (cons (f x) list)))
            ((= x a)
             (cons (f x) list))
            (else
             (iter (- x dx) (cons (* 2 (f x)) list)))))
    (* (/ dx 2) (foldl + 0 (iter b '())))))

;Simpson's rule approximation for the integral of f over range (a,b) in n divisions
(define (area-simps f a b n)
  (let ([dx (/ (- b a) n)])
    (define (iter x count list)
      (cond ((= x b)
             (iter (- x dx) (- count 1) (cons (f x) list)))
            ((= x a)
             (cons (f x) list))
            ((odd? count)
             (iter (- x dx) (- count 1) (cons (* 4 (f x)) list)))
            (else
             (iter (- x dx) (- count 1) (cons (* 2 (f x)) list)))))
    (* (/ dx 3) (foldl + 0 (iter b n '())))))

;Midpoint Rule approximation for the integral of f over range (a,b) in n divisions
(define (area-mid f a b n)
  (let ([dx (/ (- b a) n)])
    (define (iter x list)
      (let ([midp (- x (/ dx 2))])
        (cond ((= x (+ a dx))
               (cons (f midp) list))
              (else
               (iter (- x dx) (cons (f midp) list))))))
    (* dx (foldl + 0 (iter b '())))))