 Solution

ID: past-exam-of-the-numerical-analysis-course-of-the-university-of-oxford/2015/1/a/solution

For

a < b

, the one-panel trapezoidal rule is

\int_{a}^{b} f (x) d x \approx T (f) := \frac{b - a}{2} (f (a) + f (b)) .

It integrates the linear interpolation between the two endpoint samples. Indeed the affine function

ℓ (x) = \frac{b - x}{b - a} f (a) + \frac{x - a}{b - a} f (b)

T (f)

a, b

(b - a) /2

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