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Thread: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

  1. #1
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    volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

    by using triple integral , find the volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9 .
    My ans is 36 , but the ans is 144... Is my ans wrong ? volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9-img_20160912_151954.jpg
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    Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

    Hey xl5899.

    I think you may have the wrong region.

    If you look at your diagram you have two regions [look at the xy plane for the moment and forget the z-plane].

    You have two areas - one on each side of the line y = x^2.

    Try drawing a diagram and do two sets of limits for each area [i.e. each side of that line] and verify that you are indeed integrating over the correct region of area.

    If you aren't then the answer will be significantly different and I have a "hunch" you are integrating the wrong area.

    The z-values won't matter because the function is [in this case] independent of the z-value and it should just be multiplied by the height [just like a cylinder is multiplied by the height after you get the area of the cross sectional circle].
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    Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

    $\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 9$
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    Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

    Quote Originally Posted by Idea View Post
    $\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 9$
    i get 72 now , still not 144volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9-2366.png
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    Re: volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

    x from -3 to 3
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