Find the area or volume.
-Find the volume of the solid generated by revolving the area under $y = 6 e ^ { - x }$ in the first quadrant about the y-axis.
A) $12 \pi$
B) $6 \pi$
C) $24 \pi$
D) 1

Question

Quizplus · Accepted Answer

The volume of the solid generated by revolving the area under the curve $y = 6 e^{-x}$ about the y-axis can be found using the method of cylindrical shells. The integral for the volume is $V = 2\pi \int_0^\infty x(6e^{-x}) \, dx$. Solving this integral gives $V = 12\pi$.

Find the Area or Volume y=6e−xy = 6 e ^ { - x }y=6e−x

Find the Area or Volume $y = 6 e ^ { - x }$