GATE CSE 1993 | Question: 01.3

Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Comments

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.

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out of syllabus now.

Answer 1

Answer: A, B, C

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

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