Solve Complicated Integral: Get Professional Help

In summary, the conversation is about a complicated integral that the person could not solve and they are seeking help. They discuss the values of j and a, and mention using the residue theorem but it didn't match their numerical solutions. They mention trying to find the "true path" for the residue, possibly using the calculus of residues or the Fresnel integral. Finally, they discuss using the method of completing the square and share their Matlab code for the integral. They also mention using MathType5 to type their equations.
  • #1
Canerg
12
0
Hi this is very complicated integral i couldn't solve
can you help me ? how does it solve
 

Attachments

  • integral_.pdf
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  • #2
Hello, is j negative, and do you know if a is non-zero or positive? I think this integral only exists if j is non-positive and a is non-negative.
 
Last edited:
  • #3
j=sqrt(-1) and a is positive
I solved this integral numerically and i found the exact result in both Matlab and Mathematica program but I need analytical solution. I tried residue theorem but result didn't match numeric solutions.I asked some mathematicians but they couldn't find true path for the residue and i look ryzik integral book i coulnd't find.

sqrt;squareroot
Thank you for your connection
 
  • #4
Calculus of residues perhaps?
 
  • #5
yes Calculus of residues but true path is important
may be fresnel integral can solve this problem but diffucult to understand. :(
 
  • #6
You could complete the square and see if that might help you.

What do you mean by true path?
 
  • #7
can you help me to solve using square
 
  • #8
[itex]x^{2}-2rx=(x-r)^{2}-r^{2}[/itex]
 
  • #9
:) ok
i will try
 
  • #10
What program did you write those equations in if you don't mind Canerg?
 
  • #11
Hi BackEMF this is my Matlab code you can use quad instead of quade

%clc; clear all
lamda=1.55e-6;
k=2*pi/lamda;
a=10000;
r=1e-2;L=1000;
f=@(x)(1./(1+a*x.^2).*exp(i*k/(2*L)*(x.^2-2*x*r)));%% integral by numerical solution
numerical=quade(f,-inf,inf)
 
  • #12
Hi Canerg, sorry I wasn't clear enough. I meant the equations you submitted in PDF, do you mind telling me what typsetting program did you use?
 
  • #13
MathType5
 
  • #14
Thanks, sorry for imposing on your thread!
 

FAQ: Solve Complicated Integral: Get Professional Help

What is a complicated integral?

A complicated integral is an expression in calculus that involves finding the area under a curve or surface that cannot be easily evaluated using basic integration techniques. It typically involves complex functions or multiple variables.

Why is it important to solve complicated integrals?

Complicated integrals are important in many areas of science, including physics, engineering, and economics. They allow us to analyze and understand complex systems and make predictions about their behavior. In order to fully understand these systems, we need to be able to solve complicated integrals.

What are some common techniques for solving complicated integrals?

Some common techniques for solving complicated integrals include substitution, integration by parts, and partial fractions. In some cases, it may also be necessary to use more advanced techniques such as contour integration or the residue theorem.

Why might someone seek professional help for solving a complicated integral?

Solving complicated integrals can be a challenging and time-consuming process, especially for those who are not familiar with advanced integration techniques. Seeking professional help can save time and ensure accurate results, particularly for high-stakes applications like scientific research or engineering projects.

What should I look for in a professional service for solving complicated integrals?

When seeking professional help for solving complicated integrals, it is important to look for a service with experienced and knowledgeable experts in the field of mathematics and science. It is also important to ensure that the service is reputable and offers reliable and timely solutions. Additionally, consider factors such as pricing, customer reviews, and customer support when selecting a service.

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