If the Infinite Curve $y=e^{x}, x \geq 0$ , Is Rotated About the X-Axis , Find the Area

Multiple Choice

If the infinite curve $y=e^{x}, x \geq 0$ , is rotated about the x-axis , find the area of the resulting surface.

A) $\frac{\pi}{6}[\sqrt{2}+\ln (1+\sqrt{2}) ]$
B) $\frac{\pi}{6}[\sqrt{3}+\ln (1+\sqrt{3}) ]$
C) $\frac{\pi}{3}[\sqrt{2}+\ln (1+\sqrt{2}) ]$
D) $\pi[\sqrt{2}+\ln (1+\sqrt{2}) ]$
E) $\frac{\pi}{4}[\sqrt{2}+\ln (1+\sqrt{2}) ]$