Find the exact coordinates of the centroid.

Question

 

y = e^x,    y = 0,    x = 0,    x = 4

 

Find the exact coordinates of the centroid.

(x, y) = 

Answer 1

Step 1:

The function are , , and .

Centroid of the region :

If the region lies between two curves and , where , the centroid of is , where and .

Observe the graph:

Here , and on to .

Find area of the region.

.

Step 2:

The centroid is .

Substitute ,  and in .

Integral formula : .

.

Step 3:

Substitute ,  and in .

Integral formula : .

.

The centroid of the region is .

Solution:

The centroid of the region is .