Question

Find the volume of the solid of revolution formed by rotating the bounded region about the x-axis.

Answer 1

Answer:

27.11514 pi

Step-by-step explanation:

Given is a function exponential as

$f(x) = e^{-x}$

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

$\pi\int\limits^b_a {f(x)^2} \, dx$

Here a = -2 and b =1

volume = $\pi\int\limits^1_(-2) {(e^-x)^2} \, dx$

=$\pi (\frac{e^{-2x} }{-2} )\\= \frac{\pi}{2} (-e^1+e^4)\\= 27.11514 \pi$