1. Consider approximating integrals of the form
I ( f ) = ∫ √x f(x)dx
in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula
∫ √x f(x)dx ≈ w1 f(x1) ≡ I1( f )
which is exact if f(x) is any linear polynomial.
b. To find a formula
∫ √x f(x)dx ≈ w1 f(x1) + w2 f(x2) ≡ I2( f )
which is exact for all polynomial of degree ≤ 3, set up a system of four equations with unknown w1, w2, x1, x2 and find the values© BrainMass Inc. brainmass.com September 26, 2022, 9:50 pm ad1c9bdddf
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