Answer:
The volume is 3.75825.
Step-by-step explanation:
Given curves,
[tex]y=f(x)=e^{-x^2}, y=0[/tex] with [tex]x=-1,x=1[/tex]
we have to find volume of region bounded by above curves, where volume,
[tex]V=\int_{a}^{b}\pi \Big[(f(x))^2-(g(x))^2\Big]dx[/tex]
Hear, [tex]f(x)=e^{-x^2}, g(x)=0[/tex] and a=-1, b=1. Hence,
[tex]V=\int_{-1}^{1}\pi\Big[(e^{-x^2})^2-0\Big]dx[/tex]
[tex]=2\pi\int_{0}^{1}e^{-2x^2}dx[/tex]
By using integral calculator we get,
[tex]V=2\pi\int_{0}^{1}e^{-2x^2}dx[/tex]
[tex]=2\pi\times 0.5981144[/tex]
[tex]=3.75825[/tex]
Hence the result.
