Example 4-1-3 - Maple Help



Chapter 4: Integration



Section 4.1: Area by Riemann Sums



Example 4.1.3



 a) Use Maple to obtain $-\frac{125}{{n}^{3}}\sum _{i=1}^{n}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\left({i}^{2}-in\right)$ as the right Riemann sum for $f\left(x\right)=6+x-{x}^{2}$, $-2\le x\le 3$.
 b) Use Maple to evaluate this Riemann sum to .
 c) Obtain closed-form expressions for $\sum _{k=1}^{n}a$, $\sum _{k=1}^{n}k$, and $\sum _{k=1}^{n}{k}^{2}$; then use these expressions to show how the right Riemann sum becomes .







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