[R] Overlapping areas under normal distributions

[scaramouch]

Hi everyone. 

My problem: I've 4 distributions: A, B, C and D: 

#A 
mA=16.6 
sA=3.0 

#B 
mB=18.9 
sB=3.2 

#C 
mC=20.3 
sC=2.1 

#D 
mD=24 
sD=0.8 

###Graphiques ensembles 
plot(function(x) dnorm(x,mA,sA),0,40,col="orange",ylim=c(0,0.5)) 
plot(function(x) dnorm(x,mB,sB),0,40,add=T,col="green") 
plot(function(x) dnorm(x,mC,sC),0,40,add=T,col="blue") 
plot(function(x) dnorm(x,mD,sD),0,40,add=T,col="red") 

Now I've a fifth distribution X 
#X 
mX=23 
sX=0.7 
plot(function(x) dnorm(x,mX,sX),0,40,add=T,col="black") 

And I would like to know the area of the overlapping of the curve of X with
the curves of A, B, C and D (in %). 

How can I do that? 

Thank you very much, 
Kindly regards, Scaramouch 

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