# GATE1993-01.3

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1. In questions 1.1 to 1.7 below, one or more of the alternatives are correct.  Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book.  Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up.

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

1. 1
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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.

1 vote

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

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

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