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# how to do triple numerical integration in Matlab

## how to do triple numerical integration in Matlab

(OP)
Hello All:
I tried two methods as follows, but did not work correctly. Your help will be greatly appreciated.

R=2;
photonnumber=100000;
r=5;
meff=0.9;
F=0.4;
NA=pi/2
D=1.2;

1.
syms beta ceta z

bdetectpower=3*photonnumber/(4*pi*R^3)*int(int(int(exp(-sqrt(r^2+z^2-2*r*z*cos
(ceta))*meff)*F^2*(2*(1-cos(NA))*sqrt(r^2+z^2-2*r*z*cos(ceta))+3*D*sin(NA)^2*(
1+sqrt(r^2+z^2-2*r*z*cos(ceta))*meff))/(16*D*(sqrt(r^2+z^2-2*r*z*cos(ceta)))^2
)*z^2*sin(ceta),beta,0,2*pi),ceta,0,pi),z,0,R);

2.
Fun = @(beta,ceta,z) 3*photonnumber/(4*pi*R^3)*(exp(-sqrt(r^2+z^2-2*r*z*cos(
ceta))*meff)*F^2*(2*(1-cos(NA))*sqrt(r^2+z^2-2*r*z*cos(ceta))+3*D*sin(NA)^2*(1
+sqrt(r^2+z^2-2*r*z*cos(ceta))*meff))/(16*D*(sqrt(r^2+z^2-2*r*z*cos(ceta)))^2)
*z^2*sin(ceta));

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