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Q77Section I (Objective (Q1–Q80))76 of 79

Numerical Analysis — coefficients of a three-point quadrature rule

If the formula

∫x0x2f(x)dx=αf(x0)+βf(x0+h)+γf(x0+2h)\int_{x_0}^{x_2}f(x)dx=\alpha f(x_0)+\beta f(x_0+h)+\gamma f(x_0+2h)

is exact for polynomial of as high order as possible for any h>0h>0, then what are the values of α\alpha, β\beta, γ\gamma respectively?

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