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 $x=10$.

Before you start, enter the function $f(x)$ into Desmos so that you can refer to it later.

1. Evaluate $R_3$ using Desmos. Right points 4,7,10 are used.
=3[f(4)+f(7)+f(10)]
=3[3.593]
=10.779
2. Evaluate $M_3$ using Desmos
The points used are the same as before and 2.5, 5.5, 8.5 as the middle points.
=3[2.61+1.36+.981]
=3[4.965]
=14.895
4. Evaluate $L_9$ using Desmos.
The partaion points are 1-10 and the left 1-9
9$\sum$i=1 f(xi)deltaX= 19.399

4. Evaluate $R_{100}$ using Desmos. You will probably want to use the $\sum$-notation capabilities of Desmos.
I= n-1, i=0 $\sum$ f(s(i))*w
I=16.274

5. Evaluate $R_{1000}$ using Desmos.
I=n-1, i=0 $\sum$ f(s(i))*w =16.045

6. Write out an expression using a limit that will give the exact area under the curve $y=f(x)$ from $x=1$ to $x=10$.

a=10,x=1 $\sum$ [10x/x^2+1 sinx +4/x^2+1]