Question

The given curve is rotated about the y-axis. Find the area of the resulting surface.

y = 3 − x²,    0 ≤ x ≤ 2

 

Answer 1

Step 1:

The curve is , .

Re write the curve equation is .

If the curve is rotating about axis, area of the resultant surface is .

Where 

Step 2:

Substitute  and  in area formula.

Solution:

The area of the surface is  Sq-units.