Calculate Area Between 2 Curves

Question

I would like to calculate the area between the blue line and the gray diagonal line.

I can calculate the area under the blue line as:

library(zoo)    
id <- order(x)
AUC <- sum(diff(x[id])*rollmean(y[id],2))

(thanks to Calculate the Area under a Curve in R)

Any ideas how to find the area between the blue and gray line?

Thanks in advance EC

Answer 1

The area between curves is the modulus(area(under blue line) - area(under gray line)) Area under blue line is 1/2(b-a)(f(b)-f(a)) where a and b are Xs of limits and f(a),f(b) are Ys of limits. Finding area under gray line can be done using simpson's rule. see this http://en.wikipedia.org/wiki/Simpson%27s_rule They have given rule as well as implementation + accuracy provided you have arrays of xs and ys.

I hope it helps, Saurabh