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

question 61

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) \(\frac{\pi}{4}[\sqrt{2}+\ln (1+\sqrt{2})]\)

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