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Math Help - Volume of a curve rotated around the y-axis

  1. #1
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    Volume of a curve rotated around the y-axis

    Find the volume of y=4-x^2 bounded by y=0 and y=4

    Is this correct?

    y\!:\;\;V \;=\;\pi\int^4_04-y\,.dy

    V \;=\;\pi\ (4y-\frac{y^2}{2}) \bigg]^4_0

    V \;=\;8\pi\ units^3
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  2. #2
    Newbie leebatt's Avatar
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    yes your answer is correct. you could also use the method of cylindrical shells to find the volume

    x will go from x = 0 to x = 2


    the integral would be

    V \;=2\;\pi\int^2_0x(4-x^2)\,dx

    V \;=2\;\pi\int^2_04x-x^3\,dx


    V \;=2\;\pi\ (2x^2-\frac{x^4}{4}) \bigg]^2_0


    V \;=2\;\pi\ (8-4)


    V\;=8\;\pi
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  3. #3
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    Quote Originally Posted by Dr Zoidburg View Post
    Find the volume of y=4-x^2 bounded by y=0 and y=4

    Is this correct?

    y\!:\;\;V \;=\;\pi\int^4_04-y\,.dy

    V \;=\;\pi\ (4y-\frac{y^2}{2}) \bigg]^4_0

    V \;=\;8\pi\ units^3
    Yes.
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  4. #4
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    cool.
    Thanks for the confrimation.
    Now onto the next question!
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