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 .

.

Find .

As , then .

.

.

(a) Graph: 

(b) .

(c) .

(d) .

(e)

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(f) .