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Math Help - Integral Calculus

  1. #1
    Member Abu-Khalil's Avatar
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    Integral Calculus

    Find the volume between x+2y+z=4,z=x+y,x=0,y=0.

    I got , but it gives me a negative volume
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  2. #2
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    Quote Originally Posted by Abu-Khalil View Post
    Find the volume between x+2y+z=4,z=x+y,x=0,y=0.

    I got , but it gives me a negative volume
    the correct one is this: \int_0^2 \int_0^{\frac{4 - 2x}{3}} \int_{x+y}^{4-x-2y} dz dy dx.
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by Abu-Khalil View Post
    Find the volume between x+2y+z=4,z=x+y,x=0,y=0.

    I got , but it gives me a negative volume

    I think you have a mistake in your limits of integration

    x+2y+x+y=4 \iff 3y=-2x+4 \iff y =-\frac{2}{3}+\frac{4}{3}

    and x goes from 0 to 2.
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  4. #4
    Member Abu-Khalil's Avatar
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    Oh Ok, i got it. So.. i must replace the z from one equation to other, right?
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