Solving Explicit integral in symbolic form
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Hi all,
I am solving an integral brom beta (which is function of dimensionless alpha) to 1. The function f has x variable and alpha constant. I am trying this with symbolic method. I am expecting solution in terma of alpha. Theta is known. I have followed previous discussions but still I am getting error as 'Explicit integral could not be found'
Please help
clear;clc;
syms alpha positive;
syms x;
theta = 0 ;
beta = (sin (theta) + sqrt( (sin(theta).^2) + (4.*alpha.*(alpha - 1) ) ) ./(2.*alpha))
a = beta;
b = 1;
f =( (x/((alpha.*x.*x)+1-alpha)).^2 -1).^(-1/2)
int(f,x,a,b)
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Risposte (1)
Walter Roberson
il 2 Dic 2012
Can you restrict alpha even further than just "positive" ? The indefinite integral has a number of different cases, sensitive to the value of alpha, and when one tries to use that particular "a", a symbolic division by 0 is created that makes it difficult to resolve the definite integral.
The treatment with unknown alpha also introduces possibly-spurious imaginary quantities.
4 Commenti
Walter Roberson
il 3 Dic 2012
I would not count on MuPAD being able to handle the elliptic integrals, but it might be able to.
My system is still trying to find a nicer expression for the integral. So far no meaningful simplifications, other than finding a way to rewrite the single occurrence of EllipticK in terms of EllipticE and EllipticF... not sure if that counts :-(
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