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# define the pdf for X
f <- function(x) { x^2 / 9 * (0 <= x & x <= 3) }
# numerical integration gives approximation and tolerance
integrate(f, 0, 3)
integrate(f, -Inf, Inf) # same value but less precise
integrate(f, 0, 1)
integrate(f, 0, 1) %>% value() # just the approximation value
# find nearby fraction
integrate(f, 0, 1) %>% value() %>% fractions()
gf_line(y ~ x, data = tibble(x = seq(-1, 4, by = 0.01), y = f(x)),
group = ~ (x > 3)) %>%
gf_labs(y = "f(x)")
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