What is the Newton-Cotes formula in Numerical Analysis?

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What is the Newton-Cotes formula in Numerical Analysis?

The Newton-Cotes formula in Numerical Analysis is a method used for approximating definite integrals. It involves dividing the interval of integration into smaller subintervals and approximating the function within each subinterval using polynomial interpolation. The most commonly used Newton-Cotes formula is the Trapezoidal Rule, which approximates the integral by dividing the interval into trapezoids and summing the areas of these trapezoids. Other variations include Simpson's Rule and the Newton-Cotes open formula.