$\"\"$

\

The curves are $\"\"$ and $\"\"$ .

\

Graph:

\

Graph the curves $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

Observe the graph:

\

The intersection points are $\"\"$ and $\"\"$ .

\

The area bounded between $\"\"$ to $\"\"$ .

\

The upper curve is $\"\"$ .

\

The lower curve is $\"\"$ .

\

$\"\"$

\

Definite integral as area of the region:

\

If $\"image\"$ is continuous and non-negative on the closed interval $\"\"$ , then the area of the region bounded by the graph $\"image\"$ , the $\"image\"$ -axis and the vertical lines $\"image\"$ and $\"image\"$ is given by

\

$\"\"$ .

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

Apply parts of integration formula: $\"\"$ .

\

Here $\"\"$ and $\"\"$ .

\

$\"\"$

\

Apply derivate on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$ .

\

Substitute the corresponding values in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ square units.

\

Area of the region is $\"\"$ square units.

\

$\"\"$

\

Area of the region is $\"\"$ square units.