Question

Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis.

Answer 1

Step 1:

The curve is , .

Definition of the surface area:

If the curve , is rotating about -axis, then the area of the resulting surface area is given by,

.

 

Here and .

Consider .

Differentiate with respect to on each side.

Substitute , and limits of in surface area formula.

Step 2:

Solution:

Surface area of the curve is .