Consider the quadrature rule integral01 fx dx a f0 bf0 cf

Consider the quadrature rule integral_0^1 f(x) dx = a f(0) + bf\'(0) + cf(1). Determine the constants a, b, and c so that this quadrature rule has the highest degree of precision possible. Clearly show how to use this quadrature rule to approximate integral_pi^2 pi sin(x) dx. Compare this approximation to the true value by stating the relative error.

$Consider the quadrature rule integral_0^1 f(x) dx = a f(0) + bf\'(0) + cf(1). Determine the constants a, b, and c so that this quadrature rule has the highest$

Consider the quadrature rule integral01 fx dx a f0 bf0 cf

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