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Math Help - calc finding the volume

  1. #1
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    calc finding the volume

    Use the shell method to find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = tan x about the x-axis from x = 0 to x = pi/4
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    Junior Member frenzy's Avatar
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    Quote Originally Posted by harry View Post
    Use the shell method to find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = tan x about the x-axis from x = 0 to x = pi/4

    What have you tried...do you know where to start?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by harry View Post
    Use the shell method to find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = tan x about the x-axis from x = 0 to x = pi/4
    Can someone check this please, i'm kind of rusty on the shell method.

    so the shell method uses the formula:
    V = int{2pi*x*h}dx where x is the radius and h is the height. since with this problem we are rotating about the x-axis, we will do our integral with respect to y.

    y = tan(x)
    => x = arctan(y) ...........this is the height, see diagram

    so
    V = int{2pi*y*h}dy evaluated between 0 and 1
    => V = int{2pi*yarctan(y)}dy
    => V = 2pi*int{yarctan(y)}dy
    => V = 2pi [(y^2 + 1)/2 * arctan(y) - y/2] .......i used a formula forthis, but the integral can be done by parts i believe.

    now we evaluate:
    => V = 2pi(arctan(1) - 1/2)
    => V = 2pi(pi/4 - 1/2)
    => V = (pi^2)/2 - pi
    => V = (pi^2 - 2pi)/2
    Attached Thumbnails Attached Thumbnails calc finding the volume-volume2.gif  
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