Question

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.

Answer 1

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

Answer 2

DNE