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Sunday, April 12, 2020

Integration to sum

The definite integral of a continuous function f over the interval [a,b], denoted by baf(x)dx, is the limit of a Riemann sum as the number of subdivisions approach infinity.
baf(x)dx=limnni=1δxf(xi)

where δx=(ba)/n, and xi=a+δxi.

Example
2ππcos(x)dx

δx=(ba)/n=(2ππ)/n=pi/n

xi=a+δxi=π+π/ni

Therefore
2ππcos(x)dx=limnni=1πncos(π+πin)


Reference:
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/a/definite-integral-as-the-limit-of-a-riemann-sum


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