Surface area obtained by rotating the curve about the x - axis : .

2).

The function , where 2 ≤ x ≤ 5.

Surface area obtained by rotating the curve about the x - axis : .

Let, .

By Simpson\\'s rule :

Here, n = 10 and .

.

Substitute corresponding values in equation (1).

.

.

Therefore, surface area obtained by rotating the curve about the x - axis is 92.3392 sq.units.