Step 1:

\

The equations are $\"\"$ .

\

To find the point of intersection, equate the above equations $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Then the points of intersection are $\"\"$ .

\

Step 2:

\

Graph :

\

(1) Draw the coordinate plane.

\

(2) Draw the equations.

\

(3) Plot the intersection points $\"\"$ .

\

$\"\"$

\

From the graph, $\"\"$ moves from 1 to 4 and $\"\"$ moves from 4 to 1.

\

Step 3:

\

Find the area of the region.

\

Using line integral, the area of the region is $\"\"$ .

\

$\"\"$

\

$\"\"$ , and it moves from 4 to 1.

\

$\"\"$ , and it moves from 1 to 4.

\

$\"\"$

\

Solution :

\

The area of the region is $\"\"$ .