Moy Ways

News Blog in 2021

  • Contact Us
  • Home
  • Business
  • Health
  • News
    • Blog
    • Entertainment
    • Misc
    • Trending
  • Pet
  • Tech

Line Integrals in Wolfram Alpha?

November 15, 2021 by moyways Leave a Comment

Does Wolfram Alpha allow the calculation of line integrals, and if so, what would be the format to enter it in?

Table of Contents

  • Answers
  • Read Also

Answers

“Line integral” means the following (I hope).

Calculator for Line Integrals

Does Wolfram Alpha have a line integral calculator?

Is it possible in Wolfram Alpha to calculate a line integral, and if so, what is the form that has to be used? Wolfram Alpha line integrals

Line Integrals in Wolfram Alpha?
Line Integrals in Wolfram Alpha?

In this case, MathPhD is right (as we would hope with a handle such as this): this integral is a very neat application of complex variables to real-valued functions. In a first course on complex analysis, It is a standard application, but it is really quite fascinating. [1] describes this process in more detail than I care to, but in a nutshell, the idea goes like this: * Treat the integrand as a function of a complex variable, and note that, on the real axis, cos z/[(z^2 + 1)(z^2 + 2)] = Re e^(iz)/[(z^2 + 1)(z^2 + 2)] = Re f(z) * Consider the contour integral of f(z) around a semicircle, centered at the origin and oriented counter-clockwise, of radius R (if you’ve studied any multivariable calculus, this is analogous to a path or line integral in two real dimensions). * Use your complex variable theorem of choice (a calculation of residues [2] together with the Cauchy residue theorem [3] will simplify the contour integral of f around the semicircle C_R). In this integral there are two parts: a semicircular arc integral with nonzero imaginary part traced between (0, pi) and (R, 0) parameterized by (R cos t, R sin t), and an integral over a real line segment. In the context you’re accustomed to, the integral over a real segment is the same as the real integral. Infinity is the limit of this integral. We can show that because e*(iz) is bounded by 1, the contour integral over the circular part goes to 0 as R –> infinity. As a result, the complex contour integral derives its value exclusively from the integral over the real axis. Taking the real part of the integral on that axis yields the value of the desired integral, since the integral is nonzero on that axis.

See also  Whats the easiest way to give yourself a bruise?

Read Also

What is election per load on the comdata card?

Filed Under: Blog

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

  • The Growing Influence of Augmented Reality (AR) in Smartphones
    In phone
    July 18, 2023
    Augmented Reality (AR) is a technology that overlays […]
  • The Straight Truth About Hair Straighteners and Uterine Cancer
    In Health
    February 20, 2023
    The hair straightener market is currently valued at […]
  • Dinosaur National MonumentDinosaur National Monument
    In fun, Tech
    November 23, 2022
    Dinosaur National Monument. On the northwestern edge […]
  • I found a yellow round pill in my son’s room, what is it?I found a yellow round pill in my son’s room, what is it?
    In Blog
    November 10, 2021
    What is this yellow round pill I found in my […]
  • How many twisted teas can get me drunk?How many twisted teas can get me drunk?
    In Blog
    November 14, 2021
    There is no limit to how many twisted teas I can […]
  • Vaping on a budget the ultimate guideVaping on a budget the ultimate guide
    In Entertainment
    December 24, 2021
    Vaping is the method involved with breathing in fume […]
  • BackpackThings To Keep In Mind When Purchasing a Backpack
    In Trending
    March 16, 2022
    If you are someone who has recently developed a love […]
  • The Best Brands Of Women’s Bags Available To Everyone
    In Fashion
    August 18, 2022
    There is an opinion among buyers, brand bag price […]
  • Where can I find a restaurant with “All-You-Can-Eat” Crab Legs in the Dallas/Fort Worth area?Where can I find a restaurant with “All-You-Can-Eat” Crab Legs in the Dallas/Fort Worth area?
    In Blog
    November 16, 2021
    I need Crab Legs… and I need them NOW!!! […]
  • What is a good fake text message to send out saying my phone has been disconnected?What is a good fake text message to send out saying my phone has been disconnected?
    In Blog
    November 16, 2021
    (Your number) Error: Invalid Number Please resend the […]
  • Business6 Powerful Ways To Promote Your Online Business (2022) 
    In Tips
    October 10, 2022
    When you invest in promotional activities, you expect […]
  • Do you watch Law & Order? If so, what does “LUDS” mean when….?
    In Blog
    November 9, 2021
    Do you watch Law & Order? The detectives say they […]

Copyright © 2023 · Magazine Pro Theme on Genesis Framework · WordPress · Log in