Recall that ∫ a b f ( x ) d x = lim n → ∞ ∑ k = 1 n f ( x k ) Δ x {\displaystyle \int _{a}^{b}f(x)\,dx=\lim _{n\rightarrow \infty }\sum _{k=1}^{n}f(x_{k})\Delta x} , where Δ x = b − a n {\displaystyle \Delta x={\frac {b-a}{n}}} and x k = a + k Δ x {\displaystyle x_{k}=a+k\Delta x} .
Note: The sums above are called right Riemann sums, since the points at which the integrand is evaluated are the right endpoints of the subintervals [ x k , x k + 1 ] , k = 0 , 1 , … , n − 1 {\displaystyle [x_{k},x_{k+1}],k=0,1,\dots ,n-1} .
, where 
and 
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![{\displaystyle [x_{k},x_{k+1}],k=0,1,\dots ,n-1}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/40b0c7b7f73a9c518e2f2fb686f1629e007c13af)
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