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16.1 Some Rules for Approximate Evaluation: the Trapezoid Rule

16.1.1 Trapezoid Rule

We can approximate an integral by choosing n, iding the integration interval into n parts and using a Riemann sum as our approximation.

Let Ln be the result of computing the left Riemann sum in this way, and Rn be the right Riemann sum. The "trapezoid rule" is .

Here are explicit formulae for these approximate sums:


16.1.2 Simpson's Rule

Simpson's rule works only for n even and gives different weight to the f(xk) depending on the evenness or oddness of k:

Why use Simpson's rule