[tex]\int^{1}_{-1}f(x)dx = \sum^{n}_{j=-n}a_{j}f(x_{j}) [/tex](adsbygoogle = window.adsbygoogle || []).push({});

Why does [tex]\sum_{j}a_{j} = 2 [/tex] ?

I know that the a_{j}'s are weights, and in the case of [-1,1], they are calculated using the roots of the Legendre polynomial, but I don't understand why they all add up to 2.

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# Numerical Integration: Gaussian Quadrature

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