8.2 Surface Area of Revolution Question #2 (Medium)
University of Toronto St. George
8.2 Challenging Integral Applications
Surface Area of Revolution
Question #2 (Medium): Surface Area From Rotating the Function About the X-Axis
When the function is rotated about the -axis, then the radius extends vertically up. When the function
is expressed as , then use the formu∫a √ ( ) . But if the function is given in the
form of , then use ∫ √ ( ) . The part that comes from arc length can be
evaluated with because based on √ ( ) √ ( ) . So no rearrangement is
necessary and the derivative can be taken as it is.
Find the exact surface area obtained by rotating the given function about the -axis.