$\"\"$

The area bounded by the graphs are $\"\"$ , $\"\"$ and $\"\"$ .

(a) Graph the region of area:

$\"\"$ .

$\"\"$

(b)

The approximate the area of the region, begin by sub dividing the interval [a, b] into n subintervals, each of width $\"\"$ .

Partition the interval $\"\"$ into $\"\"$ subintervals, each of width $\"\"$ .

$\"\"$

Substitute $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ .

The end points are $\"\"$ .

$\"\"$

(c)

Find lower sum.

The function $\"\"$ is increasing on $\"\"$ .

The left end point is $\"\"$ .

$\"\"$ .

The lower sum is $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

(d)

Find upper sum.

The function $\"\"$ is increasing on $\"\"$ .

The right end point is $\"\"$ .

$\"\"$

The upper sum is $\"\"$ .

$\"\"$ .

$\"\"$

The lower sum is $\"\"$ .

Simplify the lower sum:

$\"\"$

Apply summation formula $\"\"$ .

$\"\"$

$\"\"$ .

The lower sum $\"\"$ .

$\"\"$

The upper sum is $\"\"$ .

$\"\"$ .

Simplify the upper sum:

$\"\"$

The upper sum is $\"\"$ .

Complete the table:

$\"\"$

$\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

$\"\"$

(f)

Find $\"\"$ .

$\"\"$

As $\"\"$ , then $\"\"$ .

$\"\"$

$\"\"$ .

Find $\"\"$ .

$\"\"$

As $\"\"$ , then $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

(a)

$\"\"$ .

(b) $\"\"$ .

$\"\"$ .

(d) $\"\"$ .

(e)

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

(f) $\"\"$ .