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Consider the definite integral ∫ from 1 to 2 (4x² + 2x + 6) dx. Let Iₑ be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is Iₛ. The percentage error is defined as e = 100 × (Iₑ − Iₛ)/Iₑ. The value of e is

1. 2.5
2. 3.5
3. 1.2
4. 0

Correct answer: 0

Solution

The percentage error is zero because Simpson's rule, when applied with an even number of subintervals, provides an exact result for polynomials of degree three or lower. Since the integrand is a polynomial of degree two, the approximation matches the exact value, resulting in no error.

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