# Integrating under a range of PDF

Dear Experts,
I have a simple PDF over X variable:

pdf = fR . signalPdf(X) + (1-fR) . bkgPdf(X)

I am fitting it and getting a fraction over full X-range. Is there a way in which I can get the fraction over a specified X range (e.g. 3.0-6.0). It is easier to do if I have functional integral over total function (pdf) and bkg function (bkgPdf), but here with pdf I am not sure.

However, I can use `createIntegral()` function, which already gives me:

X.setRange(“sigRange”,3.0,6.0)
bkg.createIntegral(X,NormSet(X),Range(“sigRange”)) = p ;
pdf.createIntegral(X,NormSet(X),Range(“sigRange”)) = q ;

But here I don’t if I can directly use the p & q fractions to compute fR(3.0 - 6.0). Please suggest if you have clear ideas to make it.

Hi @hym!

Indeed, you were right to be careful with your `p` and `q` integrals. Keep in mind that `p` is not the integral of the background component in the pdf, but the integral of the normalized background pdf in the `sigRange`.

Hence, if you want to get background integral in the signal range, you have to scale `p` by the background fraction in the total range which is `(1 - fR)`.

Put into a formula, here is how I think you can calculate the signal fraction `fR_signalRange`:

``````1 - fR_signalRange = (1 - fR) * (p / q)
``````

You could have it even easier if you use the intagrals of `sig` and `pdf`, so you don’t need the `(1 - ...)`.

I would implement that and also fit `fR_signalRange` directly by fitting only the `signalRange` as a cross check.

Let me know if this gives you the correct result and if you have further question!

Jonas

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