Numerical Integration

I'm trying to calculate numerical integration for below integral:

Numerical Integrate(f(x)*G(x) dx from alpha to beta)

that:

G(x)=Numerical Integrate(g(t) dt from gamma to x)

alpha, beta and gamma are real number, and known. thanks.

Answer 1

[Andrei Bobrov]

a = 1 % eg, input value a
b = 5 % input value b
g1 = 2 % input value g1
f = @(x)x.^2 % input function f
g = @(t)t.^3 % input function g
% solution
gq = @(x)arrayfun(@(x)quad(@(t)g(t),g1,x),x)
yourval = quad(@(x)f(x).*gq(x),a,b)

[Andrew Newell]

You can remove a couple of function handles from the last two lines:

gq = @(x)arrayfun(@(x)quad(g,g1,x),x).*f(x);

yourval = quad(gq,a,b)

[Andrei Bobrov]

Thanks Andrew! I agree with you.

[Ali Afruzi]

Thanks so much.

Answer 2

[UJJWAL]

Hi,

For Integrations and all you have more control and options in the Case of MATHEMATICA. In MATLAB it is possible to perform numerical integrations but the results are generally not as good as u get in MATHEMATICA.

In MATLAB the function you would use to integrate depends upon the kind of algorithm you want to use. There are many algorithms of numerical integrations and depending on that the function to be used would differ. For Simpson's rule we use int while for Gauss-Koncrod we use quadgk. There are other functions like quadl also. So it depends upon the method you want to use. Go through the MATLAB documentation and search for these functions. You will get the best idea. I hope it helps.

HAPPY TO HELP

UJJWAL

Answer 3

[Bjorn Gustavsson]

In addition to UJJWAL's suggestions you might benefit much from looking up the Chebfun project: http://www.mathworks.co.uk/matlabcentral/fileexchange/23972-chebfun-version-2

That offers something "halfway between symbolic and numerical" methods. Have been useful to me.

HTH