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title: 'Math 181 Miniproject 11: Riemann Sums'

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Math 181 Miniproject 11: Riemann Sums.md
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tags: MATH 181
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Math 181 Miniproject 11: Riemann Sums
===

**Overview:**   This miniproject focuses on the use of $\sum$-notation to estimate the area under a curve. Students will use Desmos to set up and evaluate Riemann sums to get the area under a curve that is not amenable to the Fundamental Theorem of Calculus. 

**Prerequisites:** Section 4.3 of *Active Calculus.*

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For this miniproject you will be estimating the area under the curve 
$$
f\left(x\right)=\left|\frac{10x}{x^2+1}\sin \left(x\right)\right|+\frac{4}{x^2+1}
$$
from $x=1$ to $x=10$.

![](https://i.imgur.com/h56UdIm.png)


Before you start, enter the function $f(x)$ into Desmos so that you can refer to it later.
(1) Evaluate $R_3$ using Desmos.
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(1) $R_{3}=10.7820774995$

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(2) Evaluate $M_3$ using Desmos.
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(2) $M_{3}=14.8990552326$
    
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(3) Evaluate $L_9$ using Desmos.
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(3) $L_{9}=18.8231531881$
   
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(4) Evaluate $R_{100}$ using Desmos. You will probably want to use the $\sum$-notation capabilities of Desmos.
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(4) $R_{100}=15.7677319241$
    
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(5) Evaluate $R_{1000}$ using Desmos.
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(5) $R_{1000}=15.9945370554$
    
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(6) Write out an expression using a limit that will give the exact area under the curve $y=f(x)$ from $x=1$ to $x=10$.
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(6) $A\left(x\right)=lim_{n->\infty}\sum_{k=1}^{n}f\left(1+1\frac{10-1}{n}\right)\cdot\frac{10-1}{n}$





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To submit this assignment click on the Publish button ![Publish button icon](https://i.imgur.com/Qk7vi9V.png). Then copy the url of the final document and submit it in Canvas.



