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The function are and .
(a)
The graph of the region bounded by functions.
(b)
The approximate the area of the region, begin by sub dividing the interval [a, b] into n subintervals, each of width .
To begin, partition the interval into subintervals, each of width ..
Substitute and .
.
The end points are .
(c)
Find lower sum.
The function is increasing over the interval.
The left end point is .
.
The lower sum is .
Substitute .
.
(d)
Find upper sum.
The function is increasing over the interval.
The right end point is .
.
Upper sum is .
.
(e)
The lower sum is .
Apply the summation formula:
.
The function is .
Apply the summation formulas.
.
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(f)
Find .
As , then .
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Find .
As , then .
.
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(a) Graph:
(b) .
(c) .
(d) .
(e)
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(f) .
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