Find the volume of the solid generated by revolving about the y-axis the region under the curve y=3e^(-2x) in the first quadrant. If the answer does not exist, enter DNE. Otherwise, round to four decimal places.
AAAaannndd the bot gets it wrong yet again!
using shells of thickness dx, we have
v = ∫[0,∞] 2πx(3e^(-2x)) dx = 6π∫[0,∞] xe^(-2x) dx = 3π/2