Answer:
The answer is "[tex]= \frac{\pi}{8}(15-41n^2 )\\[/tex]".
Step-by-step explanation:
The radius = x
the value of height is= [tex]e^{-x}[/tex]
The Formula for the volume by the shell method:
[tex]\bold{V= \int\limits^b_a {(2\pi\ rad)(height)} \, dx }[/tex]
[tex]= 2\pi \int\limits^{In 16}_0 {xe^{-x}} \, dx\\\\\\= 2\pi {(e^{-x}[-x-1])}_{0}^{In 16}\\\\ = 2\pi {(\frac{1}{16} \times (15-41n^2 ))}\\\\ = \frac{\pi}{8}(15-41n^2 )\\[/tex]
