For this problem, you will need to use the Desmos Riemann Sum Calculator. $($This link opens a new tab$/$window$.)$

Initially, the calculator shows a left Riemann sum with $n=5$ subintervals for the function $f(x)=2x1$ on the interval $1,4.$ Use the applet to compute the following sums for this function on this interval. $($The value of each Riemann sum is calculated in Line $12.)$

$L_5=,M_5=,R_5=$

$L_{25}=,M_{25}=,R_{25}=$

$L_{100}=,M_{100}=,R_{100}=$

Now use basic geometry to determine the exact area bounded by $f(x)=2x1$ and the $x-$axis on the interval $1,4.$

Exact Area $=$

Make a note of any patterns you observe.