GATE ME 2022 Set 2 — Question 13
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Engineering Mathematics → Numerical Methods → Trapezoidal & Simpson's Rules
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Question
Consider the definite integralLet be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is . The percentage error is defined as . The value of is
Correct answer
(D) 0
Solution
Simpson's 1/3 rule is exact for polynomials of degree up to 3. The integrand is a quadratic polynomial (degree 2). Therefore, the numerical integration using Simpson's rule will yield the exact value of the integral, meaning . Consequently, the percentage error .
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