$\"\"$

\

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

\

Graph the curves $\"\"$ and $\"\"$ on the same graph.

\

Graph :

\

$\"\"$

\

Observe the graph :

\

The curve intersects at $\"\"$ and $\"\"$ .

\

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

\

Where $\"\"$ and $\"\"$ .

\

The pink color represents the upper curve $\"\"$ .

\

The green color represents the lower curve $\"\"$ .

\

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

\

Note that $\"\"$ is the top half of the curve $\"\"$ .

\

Find the area bounded by the region between the curves $\"\"$ and $\"\"$ .

\

The curve intersects at $\"\"$ and $\"\"$ .

\

Therefore area bounded by the curve is $\"\"$

\

$\"\"$

\

$\"\"$

\

Find the centroid $\"\"$ :

\

$\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in above equation.

\

$\"\"$

\

The $\"\"$ -coordinate of the centroid is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in above equation.

\

$\"\"$

\

The $\"\"$ -coordinate of the centroid is $\"\"$ .

\

The centroid of the region is $\"\"$

\

$\"\"$

\

The centroid of the region is $\"\"$