Problem 5. (10 points) and - 1- sex for an The Guass-Legendre formula for approximating the integral arbitrary function

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Problem 5 10 Points And 1 Sex For An The Guass Legendre Formula For Approximating The Integral Arbitrary Function 1 (25.4 KiB) Viewed 18 times

Problem 5. (10 points) and - 1- sex for an The Guass-Legendre formula for approximating the integral arbitrary function f(x) is: 11 (5)+ () It can be verified that is the area of the trapezoid shown in the above figure (1). (7 pts) Prove that, when Rx)=2+2x+a+ax' where a, (1-0,1,2,3) are some constants, the Guass-Legendre formula obtains the exact integral; that is, prove (45) () prome (2) (3 pts) It can be shown that for any function fx), there exists a "best-area fit" line y = x + a,x for some a, and a such that this line minimizes the area difference Cr)-a,-a-xber For an arbitrary function(x), is the line through a best-area fit line? Please also explain your answer. and always