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Engineering Mathematics
Calculus
GATE 2022
Medium

Consider the definite integral ∫₁² (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

  • A2.5
  • B3.5
  • C1.2
  • 0

Explanation

Composite Simpson's rule is exact for any polynomial of degree ≤3 (its error term involves the 4th derivative, which is identically zero for a quadratic). Since the integrand 4x²+2x+6 is quadratic, Simpson's rule with any number of subintervals reproduces the exact integral, so Iₛ=Iₑ regardless of subinterval count, giving e=0.

Source: GATE ME 2022 Session 2 (ME-2) (2022)

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