Question: PROBLEM 1 (Numerical integration, as an application of linear algebra) Construct a numerical integration formula that is exact (error free) for polynomials of degree less

PROBLEM 1 (Numerical integration, as an application of linear algebra) Construct

PROBLEM 1 (Numerical integration, as an application of linear algebra) Construct a numerical integration formula that is exact (error free) for polynomials of degree less than or equal to n. (la). What is the largest possible n? Explain. (1b). For your n, determine the numerical integration formula. (1c). Show what is wrong when n is made bigger. (1d). Use your formula to estimate the area of the region under the graph of y-sin (e over interval [0, 1] PROBLEM 1 (Numerical integration, as an application of linear algebra) Construct a numerical integration formula that is exact (error free) for polynomials of degree less than or equal to n. (la). What is the largest possible n? Explain. (1b). For your n, determine the numerical integration formula. (1c). Show what is wrong when n is made bigger. (1d). Use your formula to estimate the area of the region under the graph of y-sin (e over interval [0, 1]

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