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Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work?

  1. Jan 18, 2013 #1
    Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work? :)

    Hi, everyone.

    1. Find the volume of the region between y= -2x + 4, x-axis, x=1, about the line x=1.

    I tried to post this before, but I don't think it went through!

    2. Alright, so I first drew it out, and the shape is a cone.
    Since it revolves around a y-axis, the limits should be also in terms of y.
    Every cross-section is a circle.

    So this is how I wrote it out:

    ∫0 to 4 of ∏[((-y/2) + 1)^2]dy

    ∫0 to 4 of ∏[(y^2/4) -y + 1]

    = 1/4 * (y^3)/3) - (y^2)/2) + x |0 to 4

    = ((y^3)/12) - 1/2(y^2) + x |0 to 4

    = ((4)^3)/3 - 1/2(4)^2 + 4 -(0)

    = 64/12 - 8 + 4

    = 1.33 or 4/3

    So... Is that right?
    Thank you so much for checking my work! :)
     
  2. jcsd
  3. Jan 18, 2013 #2

    Mark44

    Staff: Mentor

    Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

    What is the exact problem statement? What you have is confusing. Is the region bounded by y = -2x + 4, the x-axis, and the line x = 1 revolved about some line? You don't mention the word "revolved" in your problem statement.

    Is the region revolved about the line x = 1 or about the y-axis (the line x = 0)?
     
  4. Jan 18, 2013 #3
    Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

    Yes, it is revolved about the line x=1.

    Sorry about the confusion.
     
  5. Jan 18, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

     
  6. Jan 20, 2013 #5
    Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

    Thanks for checking it! :)

    I made a lot of mistakes in my work, but I managed to get the right answer! I'll have to fix those!
     
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