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Math Help - calc question find the volume

  1. #1
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    calc question find the volume

    How do you setup an integral to compute volume of revolution obtained by rotating the region bounded by curves y=x^2,x=1 and x=2 and the x-axis around the axis y=-1.
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  2. #2
    Junior Member frenzy's Avatar
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    Quote Originally Posted by harry View Post
    How do you setup an integral to compute volume of revolution obtained by rotating the region bounded by curves y=x^2,x=1 and x=2 and the x-axis around the axis y=-1.

    There is more than one way to do this. What method are you studying?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by harry View Post
    How do you setup an integral to compute volume of revolution obtained by rotating the region bounded by curves y=x^2,x=1 and x=2 and the x-axis around the axis y=-1.
    Again, someone check me on this. we will use the disk method.

    recall, by the disk method, V = int{Area}dx = int{pi*r^2}dx = int{pi*r*f(x)}dx

    so we have the radius from the x-axis being x^2, but we are rotating about a line 1 unit from the x-axis, so the radius we will use is 1 + x^2 . the limits as you can see from the diagram are between x= 1 and x = 2. so here goes.

    V = int{pi(1 + x^2)^2}dx evaluated between 1 and 2
    => V = pi*int{(1 + x^2)^2}dx
    => V = pi*int{1 + 2x^2 + x^4}dx
    => V = pi[x + (2/3)x^3 + (1/5)x^5] between 1 and 2
    => V = pi[(2 + (2/3)2^3 + (1/5)2^5) - (1 + 2/3 + 1/5)]
    => V = 178pi/15
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    here's a diagram
    Attached Thumbnails Attached Thumbnails calc question find the volume-volume.gif  
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