4,229 views

Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree

1. $1$
2. $2$
3. $3$
4. $4$

Notice ->

Simpson's (1/3) rule uses quadratic polynomial to approximate function but still we get correct answer till cubic polynomials.

Because cubic polynomials are symmetric around the origin so in integration + error is canceled by - error during approximation.

Please correct me if i am wrong.
out of syllabus now.

Simpson's rule actually gives exact results when approximating integrals of polynomials up to cubic degree.

Ref: http://mathworld.wolfram.com/SimpsonsRule.html

1
255 views