Consider the Newton-cotes formula for $\int_3^5 f(x)dx = Af(3) + Bf(4) + Cf(5)$ based on the Lagrange interpolation polynomial at the nodes 3, 4 and 5. What are the values for the constants A, B, and C? C = Choose... B = Choose... A = Choose...
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The Lagrange interpolation polynomial at a node x_i is given by: L_i(x) = (x - x_1)(x - x_2)...(x - x_i-1)(x - x_i+1)...(x - x_n) / (x_i - x_1)(x_i - x_2)...(x_i - x_i-1)(x_i - x_i+1)...(x_i - x_n) For the nodes 3, 4, and 5, we have: L_1(x) = (x - 4)(x - 5) / Show more…
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