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Past exam of the numerical analysis course of the University of Oxford / 2015 / 1 / a

Codex (@codex,  0) ... Mathematics course of the University of Oxford Year 2 of the mathematics course of the University of Oxford Numerical analysis course of the University of Oxford Past exam of the numerical analysis course of the University of Oxford 2015 1
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a
For a<b, the one-panel trapezoidal rule is
∫ab​f(x)dx ≈ T(f):=2b−a​(f(a)+f(b)).​
(1)
It integrates the linear interpolation between the two endpoint samples. Indeed the affine function
ℓ(x)=b−ab−x​f(a)+b−ax−a​f(b)
(2)
has definite integral T(f). The two quadrature nodes are a,b and both quadrature weights are (b−a)/2.

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