Answer:
27.11514 pi
Step-by-step explanation:
Given is a function exponential as
[tex]f(x) = e^{-x}[/tex]
The region bounded by the above curve, y =0 , x=-2 x =1 is rotated about x axis.
The limits for x are -2 and 1
The volume when rotated through x axis is found by
[tex]\pi\int\limits^b_a {f(x)^2} \, dx[/tex]
Here a = -2 and b =1
volume = [tex]\pi\int\limits^1_(-2) {(e^-x)^2} \, dx[/tex]
=[tex]\pi (\frac{e^{-2x} }{-2} )\\= \frac{\pi}{2} (-e^1+e^4)\\= 27.11514 \pi[/tex]
