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I have a set of data points, with errors (X1 , Y1 +- deltaY1) , (X2 , Y2 +-deltaY2) etc

I have the covariance matrix for these bins

I want to integrate this set of data points: SUM_i ( Y_i * X_binWidth_i )

How do I combine the errors, taking into consideretation the covariance matrix?

So I end up with a single value and a single error?

If anyone can explain or point me in the direction of some text about this that would be very helpful thanks