# How do I solve a triple integral with one integral limit in function of another variable

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Bastián Araya on 27 Sep 2022
Edited: Torsten on 28 Sep 2022
Hi, I want to integrate the following function:
fun=@(s,r,m) r*exp(-(s^2/2 + beta1*(m-mo1)))/sqrt(r^2-rmin1)
Where beta1,mo1 and rmin1 are constants previously defined (beta1= 1.72, mo1=5,rmin1=10)
These are the integration limits:
PPGA1=integral3(@(s,r,m) fun(s,r,m),-Inf,-z,rmin1,rmax1,mo1,mmax1)
Where z is in function of m and r aswell:
z=(log(0.3)-(-0.242 -0.527*(m-6) -0.778*log(r) ))/0.52
I have tried a bunch of things, but nothing works. What am I doing wrong?

Torsten on 27 Sep 2022
Edited: Torsten on 28 Sep 2022
beta1= 1.72;
mo1=5;
rmin1=10;
rmax1 = 20;
mmax1 = 10;
fun=@(r,m,s) r.*exp(-(s.^2/2 + beta1*(m-mo1)))./sqrt(r.^2-rmin1);
z = @(r,m) ((log(0.3)-(-0.242 -0.527*(m-6) -0.778*log(r) ))/0.52);
PPGA1=integral3(fun,rmin1,rmax1,mo1,mmax1,-Inf,@(r,m)-z(r,m))
PPGA1 = 0.9853
Bastián Araya on 27 Sep 2022
Thank you so much, you saved me :)

Steven Lord on 27 Sep 2022
See the "Integral over the Unit Sphere in Cartesian Coordinates" example on the integral3 documentation page for an example of how to specify the limits of integration for the one or more of the integrals as function handles.

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