What are some common numerical integration techniques?

What are some common numerical integration techniques?

Common numerical integration techniques include the Trapezoidal Rule, Simpson's Rule, and Monte Carlo integration.

Can you explain how the Trapezoidal Rule works?

Sure! The Trapezoidal Rule approximates the area under a curve by dividing it into trapezoids and summing their areas.

What are the advantages of using Simpson's Rule over the Trapezoidal Rule?

Simpson's Rule generally provides better accuracy for polynomial functions because it uses parabolic segments instead of straight lines.

When should I use Monte Carlo integration?

Monte Carlo integration is useful for high-dimensional integrals or when the integrand is complex and difficult to evaluate analytically.