# Riemann sums

Consider teh partition $P_n$ of $[1,2]$, given by $P_n=\left \{ q_0,q_1,q_2,...,q_n \right \}$ where $q_n=2$. If $f(x)=x^j$ for some positive integer $j$, then evaluate the integral $\int_{1}^{2}f(x)dx$ by calculating the limit of the corresponding lower Riemann sums.