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Calculate the Midpoint Riemann Sum

 Description Evaluate $\sum _{i=1}^{n}f\left({x}_{i}\right){\mathrm{Δx}}_{i},$the midpoint Riemann Sum of $f\left(x\right)$, $a\le x\le b$.

The Midpoint Riemann Sum

Enter $f\left(x\right)$:

 > ${{x}}^{{2}}{+}{1}$
 ${{x}}^{{2}}{+}{1}$ (1)

Enter the interval $\left[a,b\right]$:

 > $\left[{0}{,}{1}\right]$
 $\left[{0}{,}{1}\right]$ (2)

Enter the value of $n$:

 > ${4}$
 ${4}$ (3)

The midpoint Riemann sum:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{RiemannSum}\right]\left(,\left[1\right]..\left[2\right],\mathrm{method}=\mathrm{midpoint},\mathrm{output}=\mathrm{sum},\mathrm{partition}=\right)$
 $\frac{\left({\sum }_{{i}{=}{0}}^{{3}}{}\left({\left(\frac{{i}}{{4}}{+}\frac{{1}}{{8}}\right)}^{{2}}{+}{1}\right)\right)}{{4}}$ (4)

Value of the Riemann sum:

 > $\mathrm{value}\left(\right)$
 $\frac{{85}}{{64}}$ (5)

 > 
 Commands Used