Observe the graph:
\The area is bounded between and
.
The number of subintervals are .
The width of the subintervals is .
From the graph approximate the function values.
\ and
.
Find the upper sum.
\The maximum value on each subinterval occurs at the right end point.
\.
Right end points of the graph are and
.
The upper sum().
The upper sum is .
Find the lower sum.
\The minimum value on each subinterval occurs at the left end point.
\.
Left end points of the graph are and
.
The lower sum is .
The lower sum .
The area of the shaded region falls between square units and
square units.
The area of the shaded region falls between square units and
square units.