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.
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-> 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.
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You can put this solution on YOUR website! y = e^(-x)
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note that the y intercept is (0, 1) since e^(-0) = 1
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The volume(v) of the mountain is pi * integration from 0 to 1 of {f(y)}^2 * dy
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note that x = f(y) is the equation expressed in terms of y
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y = e^(-x) then
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x = ln (1/y)
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pi * integral from 0 to 1 of {ln(1/y)}^2 dy
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pi * integral from 0 to 1 ( y * (log^2(1/y) +2*log(1/y) + 2) )
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we can just evaluate it for y = 1
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note that the ln of 1 is 0
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pi * ( 1 * (0) + 2*(0) +2) = pi * 2 = 6.2832
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V = 6.2832 units^3
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