5. Consider the following two-point weighted Gaussian quadrature with the weight func- tion E13: 1m .51 .m. Ao- gas.)- {a} Find the m.- and c; in this formula. It is known that the rst several orthogonal polynomials satisfying l'mit'nhjdr =0. ifman A #,ifm=n are iim] = l,q:1{.-r]= :n L. li'Z'i-t] =32 gmI 3%. lfwe want to use decimals in your calculations, make sure to keep at least 6 digits after the decimal point. {is} Use the the quadrature rule that you get in {a} to approximate 1 ooalZm} u V'E and give the actual error. The exact integral is LSDQIMB. {c} Apprmcimate the integral in {b} using the two-point Gaussian [Gauss-legendre} quadrature. Compare the error with that in {h} Brie-},r explain why.r the Gaus- sian quadrature dog not work well. dz