Does this get you started?
f<-function(t,cx){
(abs(t-cx)*(t >= cx)+10*abs(t-cx)*(t < cx))*dbeta(t,1.05,30)
}
integrate(f,lower=0,upper=1,cx=0.4)$val # e.g., for c = 0.4
The "integrate" function integrates over the first parameter. Other
parameters can be entered as needed.
[Note: I used cx as the parameter name rather than c because 'c' has a
special meaning in R.]
-Dan
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