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Q69Section I (Objective (Q1–Q80))69 of 80

Numerical Analysis — two-point rule of maximum precision

What is the approximate value of the integral ∫01x3 dx\int_0^1 x^3\,dx, if it is obtained using the quadrature formula ∫01f(x) dx=αf(0)+βf(x1)\int_0^1 f(x)\,dx = \alpha f(0) + \beta f(x_1) which is exact for polynomials of all small degrees as high as possible?

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