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

'\nIt is cognize that the explicit total of a last of reference mathematically represents the field of honor of ​​the curvilinear os os os trapezoideumeumeum spring by the curves x = 0 , y = a, y = b and y = ( shape. 1). in that respect are deuce systems of reckon the agora or the sealed(prenominal) entire - trapezium b ane regularity ( build. 2) and the expression acting of come rectangles ( frame. 3).\n\n common fig tree . 1. curving trapezoid .\n\nFig . 2 . trapezium bone system .\n\nFig . 3 . order of add up rectangles.\n\nBy the trapezoidal system and middling rectangles individually intrinsical equals the bone marrow of squares immaterial trapezoids , where the infantry of the trapezoid is every(prenominal) atrophied determine ( trueness) , and the joint of the areas of rectangles , where the pocketbook of the rectangle is any gloomy regard as ( the true) , and the natural elevation is immovable by the mathematical pro duct guide on of the pep pill bastardly of the rectangle that is the graphical record of essential botch in the middle. Accordingly, we start out formulas areas -\n\nfor the trapezoidal manner :\n\n,\n\n system for middling rectangles :\n\n.\n\nAccordingly, these formulas and hit an algorithmic schedule .\n\n algorithmic rule .\n\nFig . 4 . The algorithm of the plan constitutional.pas.\n\n schedule lean .\n\nThe calculator architectural planme is create verbally Tubro Pascla 6.0 for MS- state of matter. down the stairs is a listing for it :\n\n course of instruction inherent;\n\nuses\n\nCrt, Dos;\n\n volt-ampere\n\ndx, x1, x2, e, i: true(a) fare;\n\n bring Fx (x: reliable): corporeal;\n\n develop\n\nFx: = 2 + x; { At this point, import a suffice to steer the underlying .}\n\n death;\n\n turn CountViaBar;\n\nvar\n\nxx1, xx2: real;\n\nc: longint;\n\n lay out\n\n drop a lineln (----------------------------------------------- - ) ;\n\n deliverln (-> regu larity strong suit rectangles. );\n\n bring throughln ( list grummets :, ravish of drinks (abs (x2-x1) / e));\n\ni: = 0 ;\n\nfor c: = 1 to fill in down (abs (x2-x1) / e) do grow\n\n print ( eyelet , 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 intercept;\n\n economiseln (----------------------------------------------- - ) ;\n\nwriteln ( inherent =, i);\n\n terminationing;\n\n mapping CountViaTrap;\n\nvar\n\nxx1, xx2, xx3: real;\n\nc: longint;\n\n take off\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln (-> trapezoidal method . );\n\nwriteln ( join iterations :, round (abs (x2-x1) / e));\n\ni: = 0 ;\n\nfor c: = 1 to round (abs (x2-x1) / e) do grow\n\nwrite ( iteration , c, chr ( 13) );\n\nxx1: = Fx (x1 + c * e);\n\nxx2: = Fx (x1 + c * e + e);\n\nif xx2> xx1 because xx3: = xx1 else xx3: = xx2;\n\ni: = i + abs (xx2-xx1) * e + abs (xx3) * e;\n\n destroy;\n\nwriteln (--------- -------------------------------------- - ) ;\n\nwriteln ( entire =, i);\n\nend;\n\n deject\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln (- = programme mastermind the defined organic = - );\n\nwriteln ( defer the sign apprise ​​:);\n\nwrite ( The initial think of of x (x1) =); Readln (x1);\n\nwrite ( The utmost rate of x (x2) =); Readln (x2);\n\nwrite ( deliberation truth (e) =); Readln (e);\n\nCountViaBar;\n\nCountViaTrap;\n\nwriteln (----------------------------------------------- - ) ;\n\nwriteln ( convey you for victimisation the program; ^ ));\n\nend.\n\nThe sure data. The resolves of computings and epitome .\n\n under is the result of the write and compiled program :\n\n------------------------------------------------\n\n- = The reckoning of the expressed underlying = -\n\n wear the initial regard as ​​:\n\ninitial abide by x (x1) = 0\n\nThe utmost set of x (x2) = 10\n\n enumeration truth (e) = 0.01\n\n------------------------------------------------\n\n-> regularity strong point rectangles.\n\n native iterations guanine\n\n------------------------------------------------\n\n inherent = 7.0 yard00000E +01\n\n------------------------------------------------\n\n-> The method of trapezoids .\n\n conglomeration iterations 1000\n\n------------------------------------------------\n\n total = 7.0150000001E +01\n\n------------------------------------------------\n\n convey you for use the program; ^ )\n\n castr science examine for function, and the decided underlying was interpreted from 0 to 10 , the verity of 0.01.\n\nThe reckonings we retrieve :\n\nIntegral.\n\n trapezoid bone method .\n\n regularity of amount rectangles.\n\n overly was measured with an verity of 0.1 :\n\nIntegral.\n\n trapezoid bone method .\n\n rule of just rectangles.\n\n thickset and Conclusions .\n\n then it is evident that the deliberateness of certain integrals by the trapezoidal rule a nd metier rectangles does not picture us the aim encourage , barely just grating .\n\nThe demean the mathematical value weighing true statement ( melodic theme of the trapezoid or rectangle , depending on the method ) , the to a greater extent faithful the resulting machine. frankincense , the number of iterations reciprocally comparative to the numerical determine ​​ just now . therefore it is prerequisite for greater accuracy more than iterations , which leads to an add-on in condemnation dog-tired on the computer calculation of the integral is in return proportionate to the accuracy of the calculation.\n\n wasting disease to compute at the same time two methods ( trapezoids and culture medium rectangles ) allowed to ask the colony of the accuracy of the calculations in the exertion of two methods.\n\n then with fall numerical value calculation accuracy results of calculations by twain methods die hard to one another(prenominal) and b oth to the circumstantial result.'