Overlapping areas under normal distributions

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?

Overlapping areas under normal distributions

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