Monte Carlo Integration is a numerical technique for estimating the definite integral of a function over a specified interval by using random sampling. This method is based on the principles of probability and statistics and provides an approach to approximate integrals, especially in cases where other methods may be challenging to apply.

**Formula:** ∫_{a}^{b} f(x) dx ≈ (b - a) * (1/n) * Σ_{i=1}^{n} f(x_i); where n is the number of random points generated within the interval [a, b], and x_i are the random points.

**Procedure:**

Generate n random points x_i within the interval [a, b].

Evaluate the function at each random point: f(x_i).

Calculate the average of these function values.

Multiply the average by the total width of the interval (b - a) to estimate the integral.

**Accuracy: **The accuracy of Monte Carlo Integration improves as the number of random points (n) increases. The law of large numbers ensures that the average value converges to the expected value as more samples are taken.

**Versatility: **Monte Carlo Integration is particularly useful for high-dimensional integrals or integrals over irregularly shaped regions where other methods may be impractical.

**Error Estimation: **The error in Monte Carlo Integration can be estimated based on statistical methods, and it typically decreases as the number of random samples increases.

Monte Carlo Integration finds applications in various fields, including physics, finance, and computational science. It leverages the power of random sampling to provide numerical approximations for integrals in situations where deterministic methods may face challenges.