Find the volume between $\displaystyle x+2y+z=4,z=x+y,x=0,y=0$. I got , but it gives me a negative volume
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Originally Posted by Abu-Khalil Find the volume between $\displaystyle x+2y+z=4,z=x+y,x=0,y=0$. I got , but it gives me a negative volume the correct one is this: $\displaystyle \int_0^2 \int_0^{\frac{4 - 2x}{3}} \int_{x+y}^{4-x-2y} dz dy dx.$
Originally Posted by Abu-Khalil Find the volume between $\displaystyle x+2y+z=4,z=x+y,x=0,y=0$. I got , but it gives me a negative volume I think you have a mistake in your limits of integration $\displaystyle x+2y+x+y=4 \iff 3y=-2x+4 \iff y =-\frac{2}{3}+\frac{4}{3}$ and x goes from 0 to 2.
Oh Ok, i got it. So.. i must replace the $\displaystyle z$ from one equation to other, right?
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