Monte Carlo Method The following computer program approximates the area of the region
Chapter 5, Problem 78(choose chapter or problem)
Monte Carlo Method The following computer program approximates the area of the region under the graph of a monotonic function and above the -axis between and Run the program for and for several values of N2. Explain why the Monte Carlo Method works. [Adaptation of Monte Carlo Method program from James M. Sconyers, Approximation of Area Under a Curve, MATHEMATICS TEACHER 77, no. 2 (February 1984). Copyright 1984 by the National Council of Teachers of Mathematics. Reprinted with permission.] 10 DEF FNF(X)=SIN(X) 20 A=0 30 B=/2 40 PRINT Input Number of Random Points 50 INPUT N2 60 N1=0 70 IF FNF(A)>FNF(B) THEN YMAX=FNF(A) ELSE YMAX=FNF(B) 80 FOR I=1 TO N2 90 X=A+(B-A)*RND(1) 100 Y=YMAX*RND(1) 110 IF Y>=FNF(X) THEN GOTO 130 120 N1=N1+1 130 NEXT I 140 AREA=(N1/N2)*(B-A)*YMAX 150 PRINT Approximate Area:; AREA 160 END
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