Question

Find the centroid of the region bounded by the given curves.

Answer 1

Step 1:

The function are and in the interval of .

The centroid of the region is .

Where and .

The area of the region is .

Upper curve is .

Lower curve is .

.

Step 2:

Find the centroid :

.

Apply integration by parts :.

Consider,

And

.

Step 3:

.

.

Solution :

The centroid of the region is .