Chapter 4.3, Problem 50E

HOW DO YOU SEE IT? Use the figure to fill in the blank with the symbol $<,>$, or $=$. Explain your reasoning.

(a) The interval [l, 5] is partitioned into n

subintervals of equal width $\Delta x$. and $x_i$ is the left endpoint of the i th subinterval.

${\displaystyle \underset{i=1}{\overset{n}{\sum }}f(x_i)\Delta x}$ ${\displaystyle {\int }_1^{5}f(x)dx}$

(b) The interval [l, 5]is partitioned into n

subintervals of equal width $\Delta x$, and $x_i$ is the right endpoint of the i th subinterval.

${\displaystyle \underset{i=1}{\overset{n}{\sum }}f(x_i)\Delta x}$ $\begin{array}{l}{\displaystyle {\int }_1^{5}f(x)dx}\\ \end{array}$