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66 lines
2.2 KiB
C++
66 lines
2.2 KiB
C++
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/*----------------- SIMPSON'S 3/8 RULE OF INTEGRATION ----------------*/
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/* THIS PROGRAM CALCULATES THE VALUE OF INTEGRATION USING
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SIMPSON'S 3/8 RULE. THE FUNCTION TO BE INTEGRATED IS,
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f(x) = 4 + 2 sin x
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INPUTS : 1) Lower and upper limits of integration.
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2) Number of intervals.
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OUTPUTS : Result of integration. */
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/*------------------------------ PROGRAM -------------------------*/
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#include<stdio.h>
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#include<math.h>
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#include<stdlib.h>
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#include<conio.h>
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void main()
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{
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double fx (double x0); /* DECLARATION OF A FUNCTION fx */
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double lo,up,f[20],h,x0,sum,result;
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int i,n;
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clrscr();
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printf("\n\t SIMPSON'S 3/8 RULE OF INTEGRATION");
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printf("\n\nEnter the lower limit of integration = ");
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scanf("%lf",&lo); /* ENTER LOWER LIMIT OF INTEGRATION */
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printf("\n\nEnter the upper limit of integration = ");
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scanf("%lf",&up); /* ENTER UPPER LIMIT OF INTEGRATION */
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printf("\n\nEnter the value of h = ");
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scanf("%lf",&h); /* ENTER THE VALUE OF h */
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n = (up - lo)/h; /* CALCULATION VALUE OF n i.e.STRIPS */
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x0 = lo;
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for(i = 0; i <= n; i++) /* LOOP TO CALCULATE VALUE OF f(x) */
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{
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f[i] = fx(x0); /* FUNCTION fx IS CALLED HERE */
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x0 = x0 + h; /* NEXT VALUE OF x IS CALCULATED HERE */
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}
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sum = 0;
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for(i = 1; i <= n-1; i++)
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{
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if(i == 3*(i/3) ) continue;
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sum = sum + 3*f[i]; /* 3 * SUM OF ORDINATES NOT MULTIPLE OF 3 */
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}
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for(i = 3; i <= n-1; i = i + 3)
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{
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sum = sum + 2*f[i]; /*2 * SUM OF ORDINATES WHICH ARE MULTIPLE OF 3*/
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}
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result = (3*h/8) * ( f[0] + f[n] + sum );
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/*Result = (3h/8) * (3 * sum of ordinates not multiple of 3
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+ 2 * sum of ordinates which are multiple of 3 ) */
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printf("\n\nThe result of integration is = %lf",result);
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}
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double fx ( double x) /* FUNCTION TO CALCULATE VALUE OF f(x) */
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{
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double f;
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f = 4 + 2 * sin(x); /* function f(x) = 4 + 2 sin x */
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return(f);
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}
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/*------------------------ END OF PROGRAM ------------------------------*/
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