SOLUTION: A "mountain" is formed by revolving the graph of {{{y = e^(-x)}}}, {{{x>=0}}}, around the y-axis. Calculate the volume of this mountain.

Question 1045314: A "mountain" is formed by revolving the graph of , , around the y-axis. Calculate the volume of this mountain.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
y = e^(-x)
:
note that the y intercept is (0, 1) since e^(-0) = 1
:
The volume(v) of the mountain is pi * integration from 0 to 1 of {f(y)}^2 * dy
:
note that x = f(y) is the equation expressed in terms of y
:
y = e^(-x) then
:
x = ln (1/y)
:
pi * integral from 0 to 1 of {ln(1/y)}^2 dy
:
pi * integral from 0 to 1 ( y * (log^2(1/y) +2*log(1/y) + 2) )
:
we can just evaluate it for y = 1
:
note that the ln of 1 is 0
:
pi * ( 1 * (0) + 2*(0) +2) = pi * 2 = 6.2832
:
********************
V = 6.2832 units^3
********************
:

RELATED QUESTIONS
1. Sketch the graph of y=3e^2x ,x=0, x=2 and x-axis. Shade the region bounded by the (answered by ikleyn,Alan3354)

A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x... (answered by solver91311)

compute the volume of the solid formed by revolving the region bounded by y=11-x, y=0 and (answered by Fombitz)

If R is a region between the graphs of the function f(x)=sinx and g(x)=cosx over the... (answered by Alan3354,ikleyn)

Let R be the region between the 𝑥-axis and the graph of y = 8/(x+1) for x>0. Let S1 be (answered by robertb)

Find the volume of the solid generated by revolving about the indicated axis the region... (answered by ikleyn)

Find the volume of the solid of revolution formed by revolving the triangle whose... (answered by Fombitz)

use the given table of values to estimate the volume of the solid formed by revolving (answered by Edwin McCravy)

Which of the following represents the volume of the solid formed by revolving the region... (answered by richard1234)