# Integral with dependent bounds

Dear all,

I have posted a question as a part of ROOT category over here . I want to post the same thing with now RooFit. Is there any way to calculate double, or actually quadrupole integrals with dependent bounds with RooFit? I want to fit this function to data later on. While this is just a representative form, the function looks something like this before I change variables:

\int_{9.5}^{10.5}da \frac{1}{x} \int_{0}^{a}dt\ t*sin(x \int_{t}^{a}dc\ c) * sph\_bessel(x,x*\int_{a}^{10000}dl\ *l)

if I change variables to have independent limits, it looks like this:

\int_{9.5}^{10.5}da \frac{1}{x} \int_{0}^{1}dt\ a*t*sin(x \int_{1}^{0}dk\ a*t*k) * sph\_bessel(x,x*\int_{1}^{0}dl\ a*l)

Can I do this over RooFit? Thanks so much for your help!

Cheers,
morbik

In the first formula, the integral over “dl” is just “(1.e8-a*a)/2.” and the integral over “dc” is just “(a*a-t*t)/2.”.

BTW. It seems to me that the “change of variables” (for “l”, “c” and “t”) in the second formula is not correct.

Dear @Wile_E_Coyote, thank you for your answer but this is a representative form as I have indicated. The real form of the function is like this:

\int_{9.5}^{10.5}da\frac{0.6}{\sqrt{3}x} \{ \int_a^1db\frac{b^{3/2}}{(1+b)^{1/2}}sin(\frac{x}{0.6\sqrt{3}}\int_b^a dc \frac{1}{c(1+c)^{1/2}})*sph\_bessel(x,\frac{x}{0.6} \int_a^{10000} dc \frac{1}{c(1+c)^{1/2}}) \}

I want to draw this function as x extends from 1 to 1000.

I didn’t want to explicitely give this as it is quite complicated. I can change the limits of the integrals to be 1 and 0 as you have suggested earlier. But the thing is that: I am just trying to understand if ROOT can perform integrals that are not of the form \int\int\int\int f(x,y,z,t)dx dy dz dt.

I hope I am able to make myself clear.

Best regards,
morbik

BTW. The integrals over “dc” can be calculated analytically. In principle, one should use clean “analytical formulas” whenever possible.