GATE CE 2020 Set 2 — Question 13
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Engineering Mathematics → Numerical Integration & ODEs → Simpson's Rule
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Question
The integralis estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statements is TRUE?
Correct answer
(D) Only Simpson's rule of estimation will give zero error.
Solution
Simpson's 1/3 rule is mathematically exact for polynomials of degree up to 3. The given integrand is a cubic polynomial (degree 3). Therefore, Simpson's rule will yield the exact value of the integral, resulting in zero error. The rectangular rule is exact for degree 0, and the trapezoidal rule is exact for degree 1; both will have non-zero errors for a cubic polynomial.
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