Numerical integration

Definition

Numerical integration involves approximating the value of definite integrals using discrete data points. It is useful when an integral cannot be solved analytically.

5 Must Know Facts For Your Next Test

1. Common methods include the Trapezoidal Rule and Simpson's Rule.
2. The Trapezoidal Rule approximates the region under the curve as a series of trapezoids.
3. Simpson's Rule provides a more accurate approximation by using parabolic segments.
4. The error in numerical integration can be reduced by increasing the number of intervals.
5. For functions that are difficult or impossible to integrate analytically, numerical methods provide practical solutions.

Review Questions

• What is the main purpose of numerical integration?
• How does Simpson's Rule differ from the Trapezoidal Rule in terms of accuracy?
• What happens to the error in numerical integration if you increase the number of intervals?

Related terms

Trapezoidal Rule:

A method for approximating definite integrals by dividing the area under a curve into trapezoids.

Simpson's Rule:

A method for approximating definite integrals that uses parabolic arcs instead of straight-line segments to better approximate areas under curves.

Definite Integral:

The evaluation of the integral from one specific point to another, providing a numerical value representing the area under a curve between two points.