The Riemann Sum is then given by the general formula: ∑i=1n fxi ⋅b−an There are five main types of Riemann Sums, depending on which point xi is chosen to determine the height: • Right Sum: the right endpoint of the subsegment • Left Sum: the left endpoint of...
Denote by F2k for k2-n<_a<_(k+l)2 -~ the set of those I~F~k with left endpoint a. Let T = inf {a: sup If(I-) - f(S~, k)]" [b((k + 4) 2-~) - b(a)[ > 2} I6F,~k or T=c~](k+2)2 ~ if no such a exists. Notice that (3.4) translates to P ( c...
Left Riemann Sum\begin{aligned} 23.57\%\end{aligned} Right Riemann Sum\begin{aligned} 26.85\%\end{aligned} Since the relative error is smaller for theleft Riemann sum, it was a better approximation. 7. a. $ \int _0^5\:3x^2\:dx \approx 106.875$ ...
Finally, recalling that the quantities παk are the interior angles of the polygon Bn, convexity requires αk≤ 1, and the formula for the sum of angles of a polygon gives ∑k=1nπαk=(n−2)π. Taking these considerations into account (1.15) becomes (1.16)f(z)=∫0z∏k=1n(...