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# define the pdf for X
f <- function(x,...) { 3 * x^2 * (0 <= x & x <= 1) }
# numerical integration gives approximation and tolerance
integrate(f,0,1)
integrate(f,0,0.5)
integrate(f,0,0.5)$value # just the approximation value
require(MASS) # for the fractions() function
fractions(integrate(f,0,0.5)$value) # find nearby fraction
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