Numerical integration with constant parameters

how to do numerical integration with constant parameters?

for example:

 f=(sin(thea)*dot([sin(thea)*cos(phia) sin(thea)*sin(phia) cos(thea)],[a*cos(thea) b*sin(thea) c*sin(thea)*cos(phia))*(3*cos(thea)*cos(thea)-1)/2

I want to do integration with thea and phia from 0-pi and 0-2*pi, respectively.

a b c are constant parameters.

What kind of functions should I use? Because like quad, dblquad can not deal with symbolic.

Thanks so much.

Answer 1

[Andrei Bobrov]

f = @(thea,phia,a,b,c)sin(thea)*dot([sin(thea)*cos(phia) sin(thea)*sin(phia) cos(thea)],[a*cos(thea) b*sin(thea) c*sin(thea)*cos(phia)])*(3*cos(thea)*cos(thea)-1)/2;

a = 1; b = 1; c = 1;  
dblquad(@(thea,phia)f(thea,phia,a,b,c),0,pi.0,2*pi);

OR for symbolic

syms thea phia a b c
f = sin(thea)*dot([sin(thea)*cos(phia) sin(thea)*sin(phia) cos(thea)],[a*cos(thea) b*sin(thea) c*sin(thea)*cos(phia)])*(3*cos(thea)*cos(thea)-1)/2;

fm = matlabFunction(f);
a = 1; b = 1; c = 1;
dblquad(@(thea,phia)fm(thea,phia,a,b,c),0,pi.0,2*pi);

[Xin]

Sorry to bother you.

Appear Error:Error: File: Untitled3.m Line: 4 Column: 45

Unexpected MATLAB expression.

Need your help.

[Andrei Bobrov]

corrected, input values for a, b, c

[VBBV]

@Xin Use a comma , instead of dot . in dblquad function for integration limits

syms thea phia a b c
f = sin(thea)*dot([sin(thea)*cos(phia) sin(thea)*sin(phia) cos(thea)],[a*cos(thea) b*sin(thea) c*sin(thea)*cos(phia)])*(3*cos(thea)*cos(thea)-1)/2;

fm = matlabFunction(f);
a = 1; b = 1; c = 1;
dblquad(@(thea,phia)fm(thea,phia,a,b,c),0,pi,0,2*pi) % use a comma for integration limits 

ans = -2.5826