Erin Lozano

2022-06-19

Find ${\int}_{-1}^{2}(5{x}^{3}+7{x}^{2}-9x+4)dx$ by Riemann sums

Alisa Gilmore

Beginner2022-06-20Added 22 answers

You will need to use the formulas

$\begin{array}{rl}\sum _{i=1}^{n}1& =n\\ \sum _{i=1}^{n}i& =\frac{n(n+1)}{2}\\ \sum _{i=1}^{n}{i}^{2}& =\frac{n(n+1)(2n+1)}{6}\\ \sum _{i=1}^{n}{i}^{3}& =\frac{{n}^{2}(n+1{)}^{2}}{4}\end{array}$

$\begin{array}{rl}\sum _{i=1}^{n}1& =n\\ \sum _{i=1}^{n}i& =\frac{n(n+1)}{2}\\ \sum _{i=1}^{n}{i}^{2}& =\frac{n(n+1)(2n+1)}{6}\\ \sum _{i=1}^{n}{i}^{3}& =\frac{{n}^{2}(n+1{)}^{2}}{4}\end{array}$

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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