Question

Find the exact area of the surface obtained by rotating the curve about the x-axis. y=sqrt(4x) 0 13 years ago

Answer 1

\[y=\sqrt{4x}~\Rightarrow ~ \frac{dy}{dx}=\frac{2}{\sqrt{4x}}\]
The area will be given by the integral
\[A=2\pi\int_0^4\sqrt{4x}\sqrt{1+\left(\frac{2}{\sqrt{4x}}\right)^2}~dx\]