how would you evaluate the Riemann Sum of $\int_a^b \frac{1}{x^2} dx$?
By the usual method, I arrived at a $x_i^*$ term of $\frac{1}{(a+i)^2}$, but am unsure of how to proceed thereafter. The sample solution provided a hint that $x_i^* = \sqrt{x_{i-1}\ x_i}\in [x_{i-1}, x_{i}]$, and I cannot tell where $\sqrt{x_{i-1}\ x_i}$ came from.
Can anyone provide some advice? Thank you very much!
