rachelrussell4241 rachelrussell4241
  • 14-01-2020
  • Mathematics
contestada

Find the volume of the solid of revolution formed by rotating the bounded region about the x-axis.
f(x)=e-x, y=0, x=-2, x=1.

Respuesta :

AlonsoDehner AlonsoDehner
  • 16-01-2020

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]

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