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Q78Section I (Objective (Q1–Q80))77 of 79

Numerical Analysis — exactness of standard rules for a cubic polynomial

For ∫01f(x)dx\int_0^1f(x)dx, where f(x)f(x) is cubic polynomial, consider the following statements:

I. Trapezoidal rule will give the exact value of the integral.\text{I. Trapezoidal rule will give the exact value of the integral.}

II. Simpson’s one-third rule will give the exact value of the integral.\text{II. Simpson's one-third rule will give the exact value of the integral.}

III. Simpson’s three-eighths rule will give the exact value of the integral.\text{III. Simpson's three-eighths rule will give the exact value of the integral.}

Which of the statements given above are correct?

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