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(define (integrate-1D L U F)
(let ((D (/ (- U L) 8.0)))
(* (+ (* (F L) 0.5)
(F (+ L D))
(F (+ L (* 2.0 D)))
(F (+ L (* 3.0 D)))
(F (+ L (* 4.0 D)))
(F (- U (* 3.0 D)))
(F (- U (* 2.0 D)))
(F (- U D))
(* (F U) 0.5))
D)))
(define (integrate-2D L1 U1 L2 U2 F)
(integrate-1D L2 U2 (lambda (y) (integrate-1D L1 U1 (lambda (x) (F x y))) )))
(define (zark U V)
(integrate-2D 0.0 U 0.0 V (lambda (X Y) (* X Y)) ))
(define (r-total N)
(do ((I 1 (+ I 1))
(Sum 0.0 (+ Sum (zark (* I 1.0) (* I 2.0)))))
((> I N) Sum)))
(define (i-total N)
(do ((I 1 (+ I 1))
(Sum 0.0 (+ Sum (let ((I2 (* (* I I) 1.0))) (* I2 I2)))))
((> I N) Sum)))
(define (error-sum-of-squares N)
(do ((I 1 (+ I 1))
(Sum 0.0 (+ Sum (let ((E (- (r-total I) (i-total I)))) (* E E)))))
((> I N) Sum)))
(begin (display (error-sum-of-squares 1000)) (newline))
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