Question

Use monte carlo integration to estimate each of the following functions using the given domain.

(a) f(x)= 1+e⁻ˣ/² / x¹/³ 0(b) g(x)= 4 / 4+x² 0(c) h(x)=x¹/⁵ 0(d) k(x)=e⁻ˣ² cosx 0

Answer 1

To estimate the given functions using Monte Carlo Integration, generate random data points within the specified domains and use them to approximate the integrals.

Step-by-step explanation:

Monte Carlo Integration is a numerical method that uses random sampling to estimate definite integrals. To estimate the given functions, we need to generate random data points within the specified domains and use them to approximate the integrals.

For example, to estimate the function f(x) = 1 + e^(-x/2) / x^(1/3) over the interval [0,1], we would randomly generate x-values between 0 and 1, calculate the corresponding y-values based on the function, and average those values to estimate the integral.

Repeat this process for each function and its specified domain to obtain the Monte Carlo approximation.