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Math Help - volume of solid

  1. #1
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    Post volume of solid

    et R be the region in the plane bounded by the x-axis and the line x=1 and the curve y= arc tan x
    determine the volume of the solid obvtained by revolving R
    about the y-axis

    any help pls
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  2. #2
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    Quote Originally Posted by alex83 View Post
    et R be the region in the plane bounded by the x-axis and the line x=1 and the curve y= arc tan x
    determine the volume of the solid obvtained by revolving R
    about the y-axis

    any help pls
    shells ...

    V = 2\pi \int_0^1 x \cdot \arctan(x) \, dx

    washers ...

    V = \pi \int_0^{\frac{\pi}{4}} 1 - \tan^2{y} \, dy


    washers looks like it may be easier to do ...

    1 - tan^2{y} = 1 - (sec^2{y} - 1) = 2 - sec^2{y}
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  3. #3
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    Smile change the revolving axis

    thanx for ur help

    if i want to change the revolving axis to x=1 how does that effect the integral limits
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  4. #4
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    Quote Originally Posted by alex83 View Post
    thanx for ur help

    if i want to change the revolving axis to x=1 how does that effect the integral limits
    doesn't affect the limits of integration ... it does affects the radius of revolution.
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  5. #5
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