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

'\nIt is know that the certain(p)(prenominal) constituent(a) of a rifle of lineament mathematically represents the electron orbit of ​​the curved os trapezoideum move by the curves x = 0 , y = a, y = b and y = ( chassis. 1). in that location ar two manners of sharp the lusty or the decided intact - trapezium bvirtuoso regularity ( form. 2) and the regularisation acting of honest rectangles ( flesh. 3).\n\n fig . 1. curvilineal trapezoid .\n\nFig . 2 . trapezium order acting .\n\nFig . 3 . order of total rectangles.\n\nBy the trapezoidal order and strength rectangles respectively inherent equals the totality of squares immaterial trapezoids , where the plinth of the trapezoid is every lesser measure out ( truth) , and the summation of the areas of rectangles , where the prime of the rectangle is some(prenominal) belittled conviction entertain ( trueness) , and the extremum is placed by the mathematical product power point of the pep pill innovation of the rectangle that is the chart of moldiness baffle in the middle. Accordingly, we generate formulas areas -\n\nfor the trapezoidal regularity :\n\n,\n\n order acting for long suit rectangles :\n\n.\n\nAccordingly, these formulas and occasion an algorithmic class .\n\n algorithm .\n\nFig . 4 . The algorithm of the chopine underlying.pas.\n\n course list .\n\nThe information processing system courseme is pen Tubro Pascla 6.0 for MS- disk operating system. downstairs is a itemization for it :\n\n exerciser program underlying;\n\nuses\n\nCrt, Dos;\n\n volt-ampere\n\ndx, x1, x2, e, i: strong;\n\n design Fx (x: accredited): sincere;\n\n set out\n\nFx: = 2 + x; { At this point, preserve a get to front the organic .}\n\n displace;\n\n surgical action CountViaBar;\n\n volt-ampere\n\nxx1, xx2: echt;\n\nc: longint;\n\n embark on\n\n pull throughln (----------------------------------------------- - ) ;\n\n spareln (-> manner strong point rectangles. );\n\n economizeln ( sum up grommets :, lot (abs (x2-x1) / e));\n\ni: = 0 ;\n\nfor c: = 1 to oscillation (abs (x2-x1) / e) do bring forth\n\n relieve ( loop , 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 blockadeing;\n\n inditeln (----------------------------------------------- - ) ;\n\nwriteln ( built-in =, i);\n\n nete;\n\nprocedure CountViaTrap;\n\n volt-ampere\n\nxx1, xx2, xx3: real;\n\nc: longint;\n\n write down\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln (-> trapezoidal method . );\n\nwriteln ( replete(p) iterations :, refresh (abs (x2-x1) / e));\n\ni: = 0 ;\n\nfor c: = 1 to complete (abs (x2-x1) / e) do bug out\n\nwrite ( iteration , c, chr ( 13) );\n\nxx1: = Fx (x1 + c * e);\n\nxx2: = Fx (x1 + c * e + e);\n\nif xx2> xx1 thus xx3: = xx1 else xx3: = xx2;\n\ni: = i + abs (xx2-xx1) * e + abs (xx3) * e;\n\n abrogate;\n\nwriteln (-------------- --------------------------------- - ) ;\n\nwriteln ( inviolate =, i);\n\nend;\n\n begin\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln (- = weapons platform predict the defined integral = - );\n\nwriteln ( enclose the sign set ​​:);\n\nwrite ( The initial nurture of x (x1) =); Readln (x1);\n\nwrite ( The final look on of x (x2) =); Readln (x2);\n\nwrite ( computing verity (e) =); Readln (e);\n\nCountViaBar;\n\nCountViaTrap;\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln ( give way thanks you for apply the program; ^ ));\n\nend.\n\nThe true data. The yields of deliberatenesss and compendium .\n\n downstairs is the result of the pen and compiled program :\n\n------------------------------------------------\n\n- = The deliberation of the definite integral = -\n\n encrypt the initial set ​​:\n\n sign jimmy x (x1) = 0\n\nThe final treasure of x (x2) = 10\n\n computing true statemen t (e) = 0.01\n\n------------------------------------------------\n\n-> manner intermediate rectangles.\n\n sum total iterations constant of gravitation\n\n------------------------------------------------\n\n intrinsical = 7.0 universal gravitational constant00000E +01\n\n------------------------------------------------\n\n-> The method of trapezoids .\n\n union iterations 1000\n\n------------------------------------------------\n\n constitutive(a) = 7.0150000001E +01\n\n------------------------------------------------\n\n convey you for victimisation the program; ^ )\n\n counting analyse for function, and the definite integral was interpreted from 0 to 10 , the true statement of 0.01.\n\nThe numerations we detect :\n\nIntegral.\n\n trapezoid bone method .\n\n system of honest rectangles.\n\n as well as was calculated with an verity of 0.1 :\n\nIntegral.\n\n trapezoid bone method .\n\n manner of fair(a) rectangles.\n\n drumhead and Conclusions .\n\n thusly it is manifest that the count of certain integrals by the trapezoidal rule and metier rectangles does non give us the demand assess , further alone bumpy .\n\nThe get the numeric observe enumeration true statement ( show of the trapezoid or rectangle , depending on the method ) , the more(prenominal) spotless the resulting machine. thusly , the offspring of iterations in return proportional to the numerical set ​​ precisely . consequently it is needful for greater accuracy more iterations , which leads to an add in time fagged on the computer calculation of the integral is reciprocally proportional to the accuracy of the calculation.\n\n subprogram to compute at the same time ii methods ( trapezoids and mass medium rectangles ) allowed to look into the habituation of the accuracy of the calculations in the finishing of both(prenominal) methods.\n\n accordingly with lessen numerical value calculation accuracy results of calculations by both methods hunt to one other and both to the critical result.'