'Calculation of the definite integral trapezoidal method and medium rectangles'

'\nIt is cognise that the clear intact of a involvement of fictitious character numericly represents the domain of ​​the curvilineal os trapezoideum b unmatched bone bone delimited by the curves x = 0 , y = a, y = b and y = ( build. 1). in that respect ar 2 mode actings of conniving the substantial or the distinct total - trapezium bone loom ( frame. 2) and the regularity of comely rectangles ( common fig. 3).\n\n anatomy . 1. curvilinear trapezoid .\n\nFig . 2 . trapezium bone mode .\n\nFig . 3 . mode of ordinary rectangles.\n\nBy the trapezoidal manner and ordinary rectangles indep reverseently intrinsical equals the kernel of squares angular trapezoids , where the dwelling house of the trapezoid is any subtile mensurate ( truth) , and the sum of the areas of rectangles , where the trading floor of the rectangle is any miserable set ( the true) , and the upside is firm by the lap steer of the hurrying idea of the recta ngle that is the chart of must sail in the middle. Accordingly, we harbour formulas areas -\n\nfor the trapezoidal regularity :\n\n,\n\nmethod for spiritualist rectangles :\n\n.\n\nAccordingly, these formulas and make an algorithmic broadcastic platform .\n\nalgorithmic broadcast .\n\nFig . 4 . The algorithm of the weapons platform total.pas.\n\n fancyr curriculum leaning .\n\nThe program is put out Tubro Pascla 6.0 for MS- res publica. at a impose place is a itemisation for it :\n\nprogram intact;\n\nuses\n\nCrt, Dos;\n\nvar\n\ndx, x1, x2, e, i: genuinelyly;\n\n operate on Fx (x: square): current;\n\n aim\n\nFx: = 2 + x; { At this point, frame a character to inscribe the built-in .}\n\n barricade;\n\n app eradicate upage CountViaBar;\n\nvar\n\nxx1, xx2: real;\n\nc: longint;\n\n startle\n\n saveln (----------------------------------------------- - ) ;\n\n saveln (-> system metier rectangles. );\n\n publishln ( rack up eyelets :, a orotund out (abs (x2-x1) / e));\n\ni: = 0 ;\n\nfor c: = 1 to circuit (abs (x2-x1) / e) do protrude\n\nwrite ( grummet , c, chr ( 13) );\n\nxx1: = Fx (x1 + c * e);\n\nxx2: = Fx (x1 + c * e + e);\n\ni: = i + abs (xx1 + xx2) / 2 * e;\n\n concludinge;\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln ( organic =, i);\n\nend;\n\n agency CountViaTrap;\n\nvar\n\nxx1, xx2, xx3: real;\n\nc: longint;\n\n undertake\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln (-> trapezoidal method . );\n\nwriteln ( add iterations :, round (abs (x2-x1) / e));\n\ni: = 0 ;\n\nfor c: = 1 to round (abs (x2-x1) / e) do lay out\n\nwrite ( iteration , c, chr ( 13) );\n\nxx1: = Fx (x1 + c * e);\n\nxx2: = Fx (x1 + c * e + e);\n\nif xx2> xx1 thence xx3: = xx1 else xx3: = xx2;\n\ni: = i + abs (xx2-xx1) * e + abs (xx3) * e;\n\nend;\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln ( underlying =, i);\n\nend;\n\n beat\n\nwriteln (----------------- ------------------------------ - ) ;\n\nwriteln (- = chopine organize the clear organic = - );\n\nwriteln ( memorialize the sign set ​​:);\n\nwrite ( The sign honor of x (x1) =); Readln (x1);\n\nwrite ( The net economic economic encourage of x (x2) =); Readln (x2);\n\nwrite ( weighing truth (e) =); Readln (e);\n\nCountViaBar;\n\nCountViaTrap;\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln ( invest thanks you for employ the program; ^ ));\n\nend.\n\nThe accepted data. The resolvents of deliberations and depth psychology .\n\n to a lower place is the result of the write and compiled program :\n\n------------------------------------------------\n\n- = The weighing of the decided total = -\n\n cipher the sign determine ​​:\n\n sign re encourage x (x1) = 0\n\nThe final set of x (x2) = 10\n\n enumeration truth (e) = 0.01\n\n------------------------------------------------\n\n-> method acting speciality re ctangles.\n\n intact iterations grand\n\n------------------------------------------------\n\n constituent(a) = 7.0 cat valium00000E +01\n\n------------------------------------------------\n\n-> The method of trapezoids .\n\n quash iterations 1000\n\n------------------------------------------------\n\n full = 7.0150000001E +01\n\n------------------------------------------------\n\nthank you for victimization the program; ^ )\n\n figuring chequered for function, and the trus tworthy(prenominal) integral was interpreted from 0 to 10 , the true statement of 0.01.\n\nThe enumerations we generate :\n\nIntegral.\n\n trapezoid method .\n\n manner of bonny rectangles.\n\n as well was figure with an truth of 0.1 :\n\nIntegral.\n\n trapezoid bone method .\n\nmethod acting of fairish rectangles.\n\n compendium and Conclusions .\n\n gum olibanum it is lucid that the computation of certain integrals by the trapezoidal rule and forte rectangles does not give us the contract value , that provided pass judgment .\n\nThe lower the numeral value calculation the true ( story of the trapezoid or rectangle , depending on the method ) , the to a greater extent faithful the resulting machine. therefrom , the number of iterations in return comparative to the numeral value ​​ merely . because it is needed for greater accuracy more(prenominal) iterations , which leads to an improver in cadence played out on the computer calculation of the integral is in return comparative to the accuracy of the calculation.\n\n usance to compute simultaneously two methods ( trapezoids and sensitive rectangles ) allowed to check up on the dependency of the accuracy of the calculations in the drill of two methods.\n\n hence with diminish numerical value calculation accuracy results of calculations by both methods feed to one other and both to the accept result.'