how to find the numerical integration in matlab

Input: syms a b phi h=int((sin(phi)/(sqrt(a+(b*sin(phi))))),phi) h1=vpa(h)

Ans: Warning: Explicit integral could not be found.

h =

int(sin(phi)/(a + b*sin(phi))^(1/2), phi)

h1 =

numeric::int(sin(phi)/(a + b*sin(phi))^(1/2), phi)

Help me to find out the mistake and tel me how to find out the numerical integration.

[Roger Stafford]

Your integral can be expressed in terms of a combination of elliptic integrals of the first and second kinds. Perhaps it would help in obtaining a symbolic expression to this effect if you declared symbols for its upper and lower limits of integration.

As Wayne has pointed out, with or without such a symbolic expression, to obtain a numerical value for the integral you will need to give specific numerical values to both these limits and to the coefficients a and b.

[Prashanth Chandrasekar]

I have the answer for the above integral in a journal,it contains a series of elliptic integrals.But i cant figure out how to get these elliptic integrals?

Answer 1

[Wayne King]

What version of MATLAB are you using? There is an integral() function for numerical integration.

Of course, you'll need values for a and b and limits of integration

a = 1;
b = 2;
f = @(x) sin(x)./sqrt(a+b*sin(x));
integral(f,0,2);

[Prashanth Chandrasekar]

using Matlab 7.10 R2010a

Answer 2

[Wayne King]

a = 1;
b = 2;
f = @(x) sin(x)./sqrt(a+b*sin(x));
quad(f,0,2);

[Wayne King]

given that you are using R2010a

[Prashanth Chandrasekar]

can we specify the various intervals between 0-2 to get different values for different values of x?in the above quad func?

[Wayne King]

yes, if you are changing the limits of integration, you get a different value for the definite integral.