EXAMPLE 2. EXAMPLE 3. EXAMPLE 4. 1 in .NET

Creator QR Code JIS X 0510 in .NET EXAMPLE 2. EXAMPLE 3. EXAMPLE 4. 1

EXAMPLE 1. EXAMPLE 2. EXAMPLE 3. EXAMPLE 4. 1
Decoding QR Code ISO/IEC18004 In VS .NET
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in VS .NET applications.
Paint Denso QR Bar Code In VS .NET
Using Barcode maker for Visual Studio .NET Control to generate, create QR-Code image in Visual Studio .NET applications.
sin x2 dx is an improper integral of the rst kind. dx is an improper integral of the second kind. x 3 0 e x p dx is an improper integral of the third kind. x
Denso QR Bar Code Decoder In VS .NET
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications.
Generating Barcode In VS .NET
Using Barcode maker for .NET Control to generate, create bar code image in Visual Studio .NET applications.
sin x sin x dx is a proper integral since lim 1. x!0 x x
Scanning Bar Code In .NET
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET framework applications.
QR Code ISO/IEC18004 Creator In C#.NET
Using Barcode generator for .NET Control to generate, create Denso QR Bar Code image in VS .NET applications.
IMPROPER INTEGRALS OF THE FIRST KIND (Unbounded Intervals) If f is an integrable on the appropriate domains, then the inde nite integrals
Denso QR Bar Code Printer In .NET
Using Barcode encoder for ASP.NET Control to generate, create Denso QR Bar Code image in ASP.NET applications.
QR Code JIS X 0510 Printer In VB.NET
Using Barcode creator for VS .NET Control to generate, create QR-Code image in VS .NET applications.
x f t dt and
EAN13 Creator In .NET
Using Barcode encoder for Visual Studio .NET Control to generate, create EAN / UCC - 13 image in Visual Studio .NET applications.
Encode Linear In .NET
Using Barcode generation for VS .NET Control to generate, create Linear Barcode image in .NET applications.
a f t dt
Barcode Drawer In Visual Studio .NET
Using Barcode generator for Visual Studio .NET Control to generate, create bar code image in Visual Studio .NET applications.
Making USD - 8 In VS .NET
Using Barcode maker for .NET framework Control to generate, create USD - 8 image in VS .NET applications.
(with variable upper and lower limits, respectively) are functions. Through them we de ne three forms of the improper integral of the rst kind. x 1 De nition (a) If f is integrable on a @ x < 1, then f x dx lim f t dt. x!1 a a a a f x dx lim f t dt: (b) If f is integrable on 1 < x @ a, then
Creating UCC-128 In None
Using Barcode creator for Word Control to generate, create GTIN - 128 image in Microsoft Word applications.
Painting Data Matrix 2d Barcode In Java
Using Barcode encoder for Java Control to generate, create DataMatrix image in Java applications.
1 x! 1 x
UPC-A Supplement 2 Generation In .NET Framework
Using Barcode encoder for Reporting Service Control to generate, create GS1 - 12 image in Reporting Service applications.
Painting GTIN - 13 In None
Using Barcode generation for Microsoft Excel Control to generate, create EAN / UCC - 13 image in Excel applications.
Copyright 2002, 1963 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
Make Barcode In Java
Using Barcode printer for BIRT Control to generate, create bar code image in BIRT reports applications.
USS Code 128 Drawer In VB.NET
Using Barcode creation for Visual Studio .NET Control to generate, create Code 128 Code Set B image in VS .NET applications.
CHAP. 12]
Code 3 Of 9 Encoder In None
Using Barcode maker for Office Word Control to generate, create Code39 image in Office Word applications.
Draw Bar Code In Objective-C
Using Barcode generator for iPhone Control to generate, create bar code image in iPhone applications.
IMPROPER INTEGRALS
(c) If f is integrable on 1 < x < 1, then 1 a 1 f x dx f x dx f x dx 1 1 a a x lim f t dt lim f t dt:
x! 1 x x!1 a
In part (c) it is important to observe that a x lim f t dt lim f t dt:
x! 1 x x!1 a
a lim f t dt
x f t dt
are not necessarily equal. 2 This can be illustrated with f x xex . The rst expression is not de ned since neither of the improper integrals (i.e., limits) is de ned while the second form yields the value 0.
EXAMPLE.
2 1 The function F x p e x =2 is called the normal density function and has numerous applications 2 in probability and statistics. In particular (see the bell-shaped curve in Fig. 12-1) 1 1 x2 p e : dx 1 2 2 1
(See Problem 12.31 for the trick of making this evaluation.)
Perhaps at some point in your academic career you were graded on the curve. The in nite region under the curve with the limiting area of 1 corresponds to the assurance of getting a grade. C s are assigned to those whose grades fall in a designated central section, and so on. (Of course, this grading procedure is not valid for a small number of students, but as the number increases it takes on statistical meaning.) In this chapter we formulate tests for convergence or divergence of improper integrals. It will be found that such tests and proofs of theorems bear close analogy to convergence and divergence tests and corresponding theorems for in nite series (See 11).
Fig. 12-1
CONVERGENCE OR DIVERGENCE OF IMPROPER INTEGRALS OF THE FIRST KIND Let f x be bounded and integrable in every nite interval a @ x @ b. Then we de ne 1 b f x dx lim f x dx
a b!1 a
where b is a variable on the positive real numbers. The integral on the left is called convergent or divergent according as the limit on the right does or 1 1 X does not exist. Note that f x dx bears close analogy to the in nite series un , where un f n , b a n 1 while f x dx corresponds to the partial sums of such in nite series. We often write M in place of
b in (1).
IMPROPER INTEGRALS
[CHAP. 12
Similarly, we de ne b
f x dx lim
a! 1 a
f x dx
where a is a variable on the negative real numbers. And we call the integral on the left convergent or divergent according as the limit on the right does or does not exist.
1 EXAMPLE 1.
dx lim x2 b!1
  1 dx 1 dx lim 1 converges to 1. 1 so that 2 2 b!1 b 1 x 1 x u cos x dx lim sin u sin a . Since this limit does not exist,
a! 1
Copyright © OnBarcode.com . All rights reserved.