# Fourier Series : Least-Squares Approximation and Mean Square Error

5. (a). Find the least squares approximation of sin(πx) over the interval [-1,1] by a polynomial of the form ao+ a1x+a2x².

(b). Find the mean square error of the approximation.

Note: Part (a) that is suppose to be sin(piex) and the polynomial is a sub 0, a sub 1, a sub 2. For some reason it wouldn't allow me to paste it in that format.

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Problem:

(a). Find the least squares approximation of sin(πx) over the interval [-1,1] by a polynomial of the form ao+ a1x+a2x².

(b). Find the mean square error of the approximation.

Solution:

a) We need to minimize the integral:

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