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| PAGE: 316 | SET: Exercises | PROBLEM: 5 |
(a)
Determine 
using right endpoints.
Observe the graph of 
.
Number of subintervals are 
.
Width of the interval is :
.
Right end points are 
and 
.
Riemann sum is 
.
.
Substitute corresponding function values in above expression observe from the graph.
Area under the graph of the function using right endpoints is 
.
.
(b)
Determine by left end points:
Number of subintervals are 
.
Width of the interval is :
.
Left end points are 
and 
.
Riemann sum is 
.
.
Substitute corresponding function values in above expression from the graph.
Area under the graph of the function using left endpoints is 
.
.
(c)
Determine by Mid points:
Number of subintervals are .
Width of the interval is :.
Mid points are 
and 
Riemann sum is .
, where 
.
.
Substitute corresponding function values in above expression from the given graph.
Area under the graph of the function using mid points is 
.
.
(a) Area under the graph of the function using right endpoints is 
.
(b) Area under the graph of the function using left endpoints is 
.
(c) Area under the graph of the function using mid points is 
.
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