Focus on Engineering It's Time for the School of Engineering $y=e^{-x}$

Multiple Choice

Focus on Engineering It's time for the School of Engineering class picture and you are the photographer! You stand at the origin with your camera and your classmates are strung out along the curve $y=e^{-x}$ from (0, 1) to $\left(3, e^{-3}\right)$ . What is the formula for the average value of the distance from you to your classmates at points (x, y) on the curve?

A) $\frac{1}{3} \int_{0}^{3} \sqrt{x^{2}+e^{-2 x}} d x$
B) $\int_{0}^{3} \sqrt{x^{2}+e^{-x}} d x$
C) $\frac{1}{3} \int_{0}^{3}\left(x+e^{-x}\right) d x$
D) $\int_{0}^{3} \sqrt{x^{2}-e^{-2 x}} d x$