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Numerical integration: Difference between revisions
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</lang>
=={{header|
{{works with|OpenComal on Linux}}
<lang Comal>
1000 PRINT "F(X)";" FROM";" TO";" L-Rect";" M-Rect";" R-Rect ";" Trapez";" Simpson"
1010 fromval:=0
1020 toval:=1
1030 PRINT "X^3 ";
1040 PRINT USING "#####": fromval;
1050 PRINT USING "#####": toval;
1060 PRINT USING "###.#########": numint(f1, "L", fromval, toval, 100);
1070 PRINT USING "###.#########": numint(f1, "R", fromval, toval, 100);
1080 PRINT USING "###.#########": numint(f1, "M", fromval, toval, 100);
1090 PRINT USING "###.#########": numint(f1, "T", fromval, toval, 100);
1100 PRINT USING "###.#########": numint(f1, "S", fromval, toval, 100)
1110 //
1120
1130 toval:=100
1140 PRINT "1/X ";
1150 PRINT USING "#####": fromval;
1160 PRINT USING "#####": toval;
1170 PRINT USING "###.#########": numint(f2, "L", fromval, toval, 1000);
1180 PRINT USING "###.#########": numint(f2, "R", fromval, toval, 1000);
1190 PRINT USING "###.#########": numint(f2, "M", fromval, toval, 1000);
1200 PRINT USING "###.#########": numint(f2, "T", fromval, toval, 1000);
1210 PRINT USING "###.#########": numint(f2, "S", fromval, toval, 1000)
1220 fromval:=0
1230 toval:=5000
1240 PRINT "X ";
1250 PRINT USING "#####": fromval;
1260 PRINT USING "#####": toval;
1270 PRINT USING "#########.###": numint(f3, "L", fromval, toval, 5000000);
1280 PRINT USING "#########.###": numint(f3, "R", fromval, toval, 5000000);
1290 PRINT USING "#########.###": numint(f3, "M", fromval, toval, 5000000);
1300 PRINT USING "#########.###": numint(f3, "T", fromval, toval, 5000000);
1310 PRINT USING "#########.###": numint(f3, "S", fromval, toval, 5000000)
1320 //
1330 fromval:=0
1340 toval:=6000
1350 PRINT "X ";
1360 PRINT USING "#####": fromval;
1370 PRINT USING "#####": toval;
1380 PRINT USING "#########.###": numint(f3, "L", fromval, toval, 6000000);
1390 PRINT USING "#########.###": numint(f3, "R", fromval, toval, 6000000);
1400 PRINT USING "#########.###": numint(f3, "M", fromval, toval, 6000000);
1410 PRINT USING "#########.###": numint(f3, "T", fromval, toval, 6000000);
1420 PRINT USING "#########.###": numint(f3, "S", fromval, toval, 6000000)
1430 END
1440 //
1450 FUNC numint(FUNC f, type$, lbound, rbound, iters) CLOSED
1460 delta:=(rbound-lbound)/iters
1470 integral:=0
1480 CASE type$ OF
1490 WHEN "L", "T", "S"
1500 actval:=lbound
1510 WHEN "M"
1520 actval:=lbound+delta/2
1530 WHEN "R"
1540 actval:=lbound+delta
1550 OTHERWISE
1560 actval:=lbound
1570 ENDCASE
1580 FOR n:=0 TO iters-1 DO
1590 CASE type$ OF
1600 WHEN "L", "M", "R"
1610 integral:+f(actval+n*delta)*delta
1620 WHEN "T"
1630 integral:+delta*(f(actval+n*delta)+f(actval+(n+1)*delta))/2
1640 WHEN "S"
1650 IF n=0 THEN
1660 sum1:=f(lbound+delta/2)
1670 sum2:=0
1680 ELSE
1690 sum1:+f(actval+n*delta+delta/2)
1700 sum2:+f(actval+n*delta)
1710 ENDIF
1720 OTHERWISE
1730 integral:=0
1740 ENDCASE
1750 ENDFOR
1760 IF type$="S" THEN
1770 RETURN (delta/6)*(f(lbound)+f(rbound)+4*sum1+2*sum2)
1780 ELSE
1790 RETURN integral
1800 ENDIF
1810 ENDFUNC
1820 //
1830 FUNC f1(x) CLOSED
1840 RETURN x^3
1850 ENDFUNC
1860 //
1870 FUNC f2(x) CLOSED
1880 RETURN 1/x
1890 ENDFUNC
1900 //
1910 FUNC f3(x) CLOSED
1920 RETURN x
1930 ENDFUNC
</lang>
{{out}}
<pre>
F(X) FROM TO L-Rect M-Rect R-Rect Trapez Simpson
X^3 0 1 0.245025000 0.255025000 0.249987500 0.250025000 0.250000000
1/X 1 100 4.654991058 4.556981058 4.604762549 4.605986058 4.605170385
X 0 5000 12499997.500 12500002.500 12500000.000 12500000.000 12500000.000
X 0 6000 17999997.000 18000003.000 18000000.000 18000000.000 18000000.000
</pre>
=={{header|D}}==
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