Question

Find the exact area of the surface obtained by rotating the curve about the x-axis.

Answer 1

Step 1 :

The surface area formula, for rotation about the x - axis is .

The function is and the interval is .

Differentiate the curve with respect to x.

Apply formula : .

.

Substitute corresponding values in .

The surface area is .

Let , then .

Evaluating boundaries :

If , then .

If , then .

Step 2 :

Substitute corresponding values in

Apply formula : .

The exact area of the surface by rotating the curve about the x - axis is 7.77 square units.

Solution :

The exact area of the surface by rotating the curve about the x - axis is 7.77 square units.