8.2 Challenging Integral Applications
Surface Area of Revolution
Question #4 (Medium): Surface Area From Rotating the Function About the Y-Axis
When the function is rotated about the -axis, the radius extends horizontally. When the function is
expressed as , then ∫ √ ( ) . But if the function is given as , then
∫ √ ( ) . The expression from arc length can be evaluatedjust as well
because √ ( ) √ ( ) . The function does not have to be rearranged,
and the derivative can be taken as it is.
Find the exact surface area obtained by rotating the given function about the -axis.