Question: A popular method of numerical integration involves Gaussian integration; it is used in finite-element calculations which are well used in most of engineering. As

A popular method of numerical integration – involves Gaussian integration; it is used in finite-element calculations which are well used in most of engineering. As a simple example, the numerical integral over the interval –1 ≤ x ≤ 1 is written

[ f(x)dx = Cf(x) + Cf(x) and the formula is made exact for the four functions f = 1, f = x, f = x and f = x,

Use Gaussian elimination to reduce the equations and hence deduce that the equations are only consistent if x₁ and x₂ are chosen at the ‘Gauss’ points ±1/√3.

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