(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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