how to find the numerical integration in matlab

Question

Prashanth Chandrasekar 2014-2-3

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评论： Wayne King 2014-2-4

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.

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Roger Stafford 2014-2-3

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 2014-2-4

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?

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Answer 1

Wayne King 2014-2-3

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编辑：Wayne King 2014-2-3

在 MATLAB Online 中打开

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);

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Prashanth Chandrasekar 2014-2-3

using Matlab 7.10 R2010a

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Answer 2

Wayne King 2014-2-3

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在 MATLAB Online 中打开

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

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Prashanth Chandrasekar 2014-2-4

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 2014-2-4

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

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