how to create barcode in asp.net c# FIGURE I73 An illustrotion meon (o)discreie (b)continuous for of the ond dotc in Software

Encoder QR in Software FIGURE I73 An illustrotion meon (o)discreie (b)continuous for of the ond dotc

FIGURE I73 An illustrotion meon (o)discreie (b)continuous for of the ond dotc
Printing QR Code ISO/IEC18004 In None
Using Barcode generation for Software Control to generate, create QR image in Software applications.
QR Code JIS X 0510 Scanner In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
INTEGRATION NUMERICAL FORMUTAS
QR Code Creation In Visual C#
Using Barcode generator for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in Visual Studio .NET applications.
QR Code Encoder In Visual Studio .NET
Using Barcode maker for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.
Integralsare also employedby engineers and scientists evaluate totalamount0r to the quantity ofa given physicalvariableThe integralmay be evaluated over a line, anNea,sr a volumeFor example total massof chemicalcontained a reactor girenasth the in is product of the concentration chemicaland the reactorvolume, or of Mass : concrentration volume x where concentration has urrits mass per volume However, suppose of that concentration varies from location to location within the reactorIn this case,it is necessary sumthe to productsof local concentrations and corresponding c; elementalvolumes A Vi:
Painting QR Code JIS X 0510 In .NET Framework
Using Barcode printer for VS .NET Control to generate, create Quick Response Code image in .NET applications.
Encoding QR In Visual Basic .NET
Using Barcode maker for Visual Studio .NET Control to generate, create Denso QR Bar Code image in .NET applications.
: Mass I,on
Making Bar Code In None
Using Barcode drawer for Software Control to generate, create bar code image in Software applications.
EAN 128 Encoder In None
Using Barcode creator for Software Control to generate, create USS-128 image in Software applications.
whererr is the numberof discrete volumes For the continuous wherec(x, y, t) isa case, known function andx, y, and : are independent positionin Cartesian variables designating integrationcan be usedfor the samepurpose: coordinates, Mass:
ANSI/AIM Code 39 Creation In None
Using Barcode encoder for Software Control to generate, create Code-39 image in Software applications.
Encoding Data Matrix ECC200 In None
Using Barcode printer for Software Control to generate, create ECC200 image in Software applications.
III,,ttt
Encoding Bar Code In None
Using Barcode maker for Software Control to generate, create bar code image in Software applications.
Creating UPCA In None
Using Barcode printer for Software Control to generate, create UPC-A image in Software applications.
t , z ) d r d v d z
Encoding GS1 - 8 In None
Using Barcode creator for Software Control to generate, create EAN8 image in Software applications.
Printing Code 3 Of 9 In Visual Studio .NET
Using Barcode creation for Visual Studio .NET Control to generate, create Code39 image in .NET applications.
Mirss: lllrtvtdV
DataMatrix Reader In Visual C#.NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.
GTIN - 13 Generator In Java
Using Barcode creator for BIRT Control to generate, create UPC - 13 image in BIRT reports applications.
JJJ v
Making Barcode In None
Using Barcode generator for Font Control to generate, create bar code image in Font applications.
Drawing Bar Code In None
Using Barcode generator for Online Control to generate, create barcode image in Online applications.
which is referredto as a volume integrctL Notice the strong analogybetweensummation and integration Similarexamples could be givenin otherfieldsof engineering science examand For ple, the total rate of energy transferacrossa plane where the flux (in caloriesper square per centimeter second) a lunctionof positionis givenby is
Scan Bar Code In VS .NET
Using Barcode reader for .NET framework Control to read, scan read, scan image in .NET framework applications.
Generating Barcode In .NET Framework
Using Barcode generation for VS .NET Control to generate, create barcode image in Visual Studio .NET applications.
Flux:llnu*ae
" "r which is referredto as an areal integral whereA : areo Thesearejust a few of the applications integrationthat you might taceregukuly of in the pursuit of your profession When the functionsto be analyzedare simple,you will normally chooseto evaluatethem analyticallyHowever, it is often difficult or impossible whenthe functionis complicated, is typicallythe casein morerealistic as In examplesaddition, the underlyingfunction is often unknownand definedonly by measurementdisat you must have the ability to obtain approximate values crete points For both thesecases, for integralsusing numericaltechniques described as next
NEWTON-COTES FORMULAS
The Newton-Cotesformulas the most common numerical integrationschemes, are They are basedon the strategyof replacingn complicated function or tabuiated datawitha polynomial that is easyto integrate:
7b 7b
I:lf(r\dr=1f(,r\tlx
FORMULAS I 22 NEWTON-COTES
where ll, (,r) : a polynomial of'the form a,, rtr"I la,tx" fr(r):a0+alx +"'+
(179)
wheren is the order of the polynomialFor example,inFig 174a, a first-orderpolynomial (a straightline) is usedas an approximation Fig 174b,a parabolais employedfor the In samepurpose using a series polynomialsappliedpiecewise of The integralcan also be approximated of to the function or data over segments constantlength For example,in Fig 175,three
FIGURE 4 I7 (o) ine by The opproximction integrol thecreounder c stroight ond(b)o porobolo of on
"f(;r)
f (tt)
FIGURE 5 I7 three by oreo under stroightline segmenis The opproximotion integro fhe of on
l(r)
FORMULAS NUMERICAL INTEGRATION
FIGURE I76 inlegrotion The difference behween closed ib)open ond formulos {o)
polynomialscan are straight-linesegmerlts usedto approximate integralHigher-order the be utilized for the samepurpose formulas al'eavailable closedlorns The Closedand openforms of tlre Newton-Cotes are those where the data points at the beginning and end of the limits of integration ac known (Fig 176a)The openfornrs have integrationlimits that extendbeyond rangc the the material m of the data (Fig 176b)This chapteremphasizes closedforms However, formulas is briefly introducedin Section177 open Newton-Cotes
RUIE 173 THETRAPEZOIDAT
formulas con+ The trapezoidalruleis the first of the Newton-Cotes It closedintegration sponds the casewherethe polynomialin Eq (178)is first-order: to
l""lt^
f (b) - f (a) (r- I , , ")]d, D-0
s T h e r e s u l t f t h e i n t e g r a t i oin o l:(b kl) + [(b) - r r ) f' 2
(1710
which is calledthe trapezoidalrule Geometrically,the trapezoidalrule is equivalentto approximatingthe area fu of g trapezoidunderthe straightline connectin I O1 andJ @) inFig l7 7 Recall from geor etry that the formula for computingthe areaof a trapezoidis the heighttimestheaverage of the bases onrcase,the conceptis the sarrie the trapezoidis on its side In but Therefog the integralestimatecan be represented as / - width x ,verageheight
EXAM
173 THETRAPEZOIDAL RULE
F I G U R E7 7 I Grophicol depicrionthe of tropezoidol rule
I : (b - rr) x average height
(r7r3)
where, fbr the trapezoidalrule, the average height is the averageof the function valuesat the end points,or lf (o) + J @)112 All the Newton-cotes closed lormulas can be expressed in the generalfbrmat of Eq' ( 17'13)' That is, they difl'er only with respect to the formulationof the average height
| 731 Error of the TropezoidolRule
when we employ the integral under a straight-rine segmentto approximatethe integral undera curve,we obviouslycan incur oo, that rnay be substantial (Fig l 7g) An esti_ mafe forthe local truncationenorof a "n singleapplicationof the trapezoidal rule is E,:--;f"tE)tl,
Copyright © OnBarcode.com . All rights reserved.