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Math Help - proof an integral

  1. #1
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    Question proof an integral

    show in the notation of the figure that the volume of the gasoline that fills the tank to depth d is

    V= 2L integral {-r , -r+d} sqrt (r^2 - y^2)dy


    how can i show that ?
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  2. #2
    Eater of Worlds
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    Let R=radius of tank and d=depth of gas.

    The circle that makes up the ends of the tank can be represented by

    x=\pm\sqrt{R^{2}-y^{2}}

    Integrate this over the depth of the gas.

    \int_{-R}^{d-R}\sqrt{R^{2}-y^{2}}dy

    Multiply by L for the length of the tank and multiply by 2 to include the whole circle and not just the upper portion.

    2L\int_{-R}^{d-R}\sqrt{R^{2}-y^{2}}dy
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  3. #3
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    Question which method to use

    which method should i use to evaluate the above integral ??

    thnx
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  4. #4
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    Quote Originally Posted by alex83 View Post
    which method should i use to evaluate the above integral ??

    thnx
    Maths is not a spectator sport. Review the methods you have been taught. What have you tried? Where do you get stuck?
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