## 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));

bdetectpower= triplequad(Fun,0,2*pi,0,pi,0,R)

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));

bdetectpower= triplequad(Fun,0,2*pi,0,pi,0,R)