Simpson's rule is a numerical integration technique used to approximate the definite integral of a function over a specified interval. It uses the idea of divid...
Simpson's rule is a numerical integration technique used to approximate the definite integral of a function over a specified interval. It uses the idea of dividing the interval into smaller subintervals and approximating the area of each subinterval with a rectangular shape.
The rule uses the following steps to approximate the definite integral:
Divide the interval [a, b] into n subintervals of equal width (h = (b - a) / n).
For each subinterval, approximate the area of the subinterval with a rectangle with height h and base equal to the width of the subinterval (h).
Sum the areas of all rectangles to get an approximation of the total area.
Repeat steps 2 and 3 for all subintervals and add the results to get a final estimate of the definite integral.
Simpson's rule is a powerful and widely used numerical integration technique that provides a balance between accuracy and computational efficiency. It is often used in various engineering, scientific, and financial applications where precise estimates of definite integrals are required