I don't get this...
-My teacher never told me how to do the Midpoint Riemann Sum
-WE don't have the graph, is there a way to solve the problem w/o graphing??
Integral from 1 to 2 of $\displaystyle x{{^-2}}$
n = 4
$\displaystyle f(x) = \frac{1}{x^2}$
midpoint Riemann sum ... height of each rectangle is the function value evaluated at the midpoint of each subinterval.
for example, the first subinterval starts at $\displaystyle 1$ and ends at $\displaystyle \frac{5}{4}$ ... midpoint x-value is $\displaystyle \frac{1+\frac{5}{4}}{2} = \frac{9}{8}$
$\displaystyle \int_1^2 \frac{1}{x^2} \, dx \approx \frac{2-1}{4}\left[f\left(\frac{9}{8}\right)+f\left(\frac{11}{8}\righ t)+f\left(\frac{13}{8}\right)+f\left(\frac{15}{8}\ right)\right]$