Find the surface area of an ornamental light bulb designed by revolving the graph of y=(1/3)x^(1/2)-x^(3/2), on the interval 0 to 1/3, about the x axis.
Find the surface area of an ornamental light bulb designed by revolving the graph of y=(1/3)x^(1/2)-x^(3/2), on the interval 0 to 1/3, about the x axis.
I assume you're familiar with the formula and can calculate dy/dx.
Start by showing that $\displaystyle \sqrt{\left(\frac{dy}{dx} \right)^2 + 1} = \frac{1}{6} \left( x^{-1/2} + 9 x^{1/2}\right)$.