∫baf(x)dx=limn→∞n∑i=1δx⋅f(xi)
where δx=(b−a)/n, and xi=a+δx⋅i.
Example
∫2ππcos(x)dx
δx=(b−a)/n=(2π−π)/n=pi/n
xi=a+δx⋅i=π+π/n⋅i
Therefore
∫2ππcos(x)dx=limn→∞n∑i=1πn⋅cos(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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