solve-this-using-Riemann-sum-f-x-2x-0-4-for-n-4-

Question Number 104359 by bemath last updated on 21/Jul/20

s o l v e t h i s u s i n g R i e m a n n

s u m f (x) = 2 x; [0, 4] f o r n = 4

Answered by Ar Brandon last updated on 21/Jul/20

\int_{0}^{4} 2 x d x = \lim_{n \to \infty} \frac{4 - 0}{n} \underset{k = 1}{\sum^{n}} 2 (0 + \frac{4 k}{n}) = \lim_{n \to \infty} \frac{4}{n} \underset{k = 1}{\sum^{n}} \frac{8 k}{n}

= \lim_{n \to \infty} \frac{32}{n^{2}} \cdot \frac{n (n + 1)}{2} = \underset{n \to \infty}{\lim 16} (1 + \frac{1}{n}) = 16