Question

The region above the x-axis and below the curve 𝑦 = 𝑒 −𝑥 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ ∞ is rotated around the x-axis. Find the volume of the solid generated.

Answer 1

$V=|\int^{\infin}_0\pi(e^{-x})^2dx|=|\frac{\pi}{2e^{2x}}|^{\infin}_0|=\pi/2$