Question

Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.

y = 2x,  y = 0,   x =1

Answer 1

Step 1:

The functions are , and

The region bounded by the curves :

Observe the figure:

The area of the region bounded by the curves is A  = 1.

Step 2:

The centroid of the region is .

.

Substitute and in above equation.

Step 3:

.

Substitute and in above equation.

.

The centroid of the region is

Step 4 :

The graph of the functions and the centroid :

Solution :

The centroid of the region is

The graph of the functions and the centroid :