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Thread: 2 unit integration

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    New Member otakuworld's Avatar
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    2 unit integration

    Find the shaded area is rotated around the y-axis. Find the volume of the solid formed.
    This is the question. I don't understand how I keep getting this wrong! I used the formulas in the pic
    18.jpg
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    Last edited by otakuworld; 7 Nov 2017 at 11:40 PM.

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    Senior Member jazz519's Avatar
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    Re: 2 unit integration

    https://imgur.com/a/C2jMf
    https://imgur.com/a/JHJR6
    (if I didn't do any silly stuff should be right)
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    Re: 2 unit integration

    i'm not sure if this is right.I'm don't know if I even used the right formulas..on the sheet the answer says its 3π/2

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    Re: 2 unit integration

    Quote Originally Posted by otakuworld View Post
    i'm not sure if this is right.I'm don't know if I even used the right formulas..on the sheet the answer says its 3π/2
    n? we have values though. For ur equation can't be write because its around the y axis for the volume (so needs to be dy)
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    Re: 2 unit integration

    no sorry for some reason that Pi came out as an n

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    Re: 2 unit integration

    Quote Originally Posted by otakuworld View Post
    no sorry for some reason that Pi came out as an n
    oh right. I'll check my working again
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    Senior Member jazz519's Avatar
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    Re: 2 unit integration

    Oh lol my idiot brain changed a nine to a four and forgot the square (need to sleep rip)

    So its v = pi (from 0 to 4) (4-y-y^2/9)dy
    = pi (4y-y^2/2-y^3/27) (from 0 to 4)
    = pi (16-8-64/27)
    = pi (152/27)(which still isn't right lol)
    Last edited by jazz519; 8 Nov 2017 at 12:29 AM.
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    Re: 2 unit integration

    Quote Originally Posted by otakuworld View Post
    no sorry for some reason that Pi came out as an n


    π.
    pikachu975, 1729 and otakuworld like this.

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    Re: 2 unit integration

    Oh right I remember how to do this now gotta split the volumes (I'll post the pic in a sec)
    Last edited by jazz519; 8 Nov 2017 at 12:38 AM.
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    Re: 2 unit integration

    Volume = pi [integral(0 to 3) (y^2 /9)dy + integral(3 to 4) (4-y)dy]
    = pi [y^3 / 27](0 to 3) + [4y - y^2 /2](3 to 4)]
    = pi [27/27 - 0 + 16 - 16/2 - 12 + 9/2]
    = 3pi/2 u^3
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    Re: 2 unit integration

    I'll skip the area for now but thank you so much
    I don't have to stay up

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    Re: 2 unit integration

    thank you!

  14. #14
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    Re: 2 unit integration

    Quote Originally Posted by otakuworld View Post
    I'll skip the area for now but thank you so much
    I don't have to stay up
    Oh for the area do the same splitting thing from zero to three for the y=3x (which is a triangle), and three to four for the y= 4-xsqared
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