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| PAGE: 270 | SET: Exercises | PROBLEM: 86 |
The function 
is increasing on the interval 
.
The interval 
is divided into 
subintervals.
(a)
Find the left end points.
The width 
.
Substitute 
and 
.
.
The left end point is 
.
Substitute 
and 
.
.
The left end point at the first subinterval.
Substitute 
in 
.
.
The left end point at the last subinterval.
Substitute 
in 
.
.
The left end points of the first and last subintervals are 
and 
.
(b)
Find the right end points.
The left end point is 
.
Substitute and .
.
The right end point at the first subinterval.
Substitute 
in 
.
.
The right end point at the second subinterval.
Substitute 
in 
.
.
The right end points of the first and last subintervals are 
and 
.
(c)
When using the right end points on an increasing function the rectangles will above the graph of the function .
The upper right corner of each rectangle lies on .While the upper left corner of is above .
Consider 
over the interval .
Graph the function:
.
Observe the graph:
In the right end points upper right corner of each rectangle lies on .While the upper left corner of is above .
(d)
Consider a constant function 
over interval 
.
Graph the function:
.
Observe the graph:
If a function is constant on the interval, then the height of rectangles are same.
(a) The left end points of the first and last subintervals are and .
(b) The right end points of the first and last subintervals are and .
(c)
In the right end points upper right corner of each rectangle lies on .While the upper left corner of is above .
(d) If a function is constant on the interval, then the height of rectangles are same.
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