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

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.