Quod Erat Demonstrandum

2008/10/22

Integrate polynomial of degree less than 4

Filed under: Additional / Applied Mathematics — johnmayhk @ 8:30 下午
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To find the definite integral of a polynomial of degree less than 4, we can use the following formula.

\int_a^b p(x)dx = \frac{b - a}{6}[p(a) + 4p(\frac{a+b}{2}) + p(b)]

e.g.

\int_2^4 (x-2)(x-4)(x-7)dx = \frac{4-2}{6}[0 + 4(3-2)(3-4)(3-7) + 0] = \frac{16}{3}

Nothing special, it is just something about Simpson’s rule.

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