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I have been trying to solve this Beta distribution problem for quite some time without success. I can get as far as getting the 20 value, but I just cannot tell how the f(x)dx = .3672 is obtained. Underneath is a short description of the problem and on attachment the approach I have used.

If anyone can help, it is most appreciated.

Problem:

The fuel used by a neighborhood is refilled every month. After several months of measurements, it is seen that the proportion of fuel reserves being used, monthly, can be modelled by a Beta distribution B(4,2). Estimate the probability that, in a given month, more than 75% of the fuel reserve is used.

f(x) = 20x^3(1-x) si 0<x<1 y f(x)=0

f(x)dx = .3672