Question: Experiment on Monte Carlo Integration To approximate the integral 1 0 f(x) dx calculate a Monte Carlo sum 1 N N i=1 f(xi)

Experiment on Monte Carlo Integration To approximate the integral 1 0 f(x) dx calculate a Monte Carlo sum 1 N N i=1 f(xi) for f(x)=5x4 and, for example, N = 100000 random numbers xi ∼ U[0, 1]. The absolute error behaves like cN −1/2. Compare the approximation with the exact integral for several N and seeds to obtain an estimate of c.

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