Calculate volume

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November 8th 2008, 09:07 AM
Apprentice123

Calculate volume

The volume of solid limited by: $2y^2=x$ , $\frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1$ , $z=0$ and $y=0$

Answer:
$\frac{17}{5}$
November 8th 2008, 10:06 AM
Mathstud28

Quote:

Originally Posted by Apprentice123

The volume of solid limited by: $2y^2=x$ , $\frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1$ , $z=0$ and $y=0$

Answer:
$\frac{17}{5}$

Maybe I am making a computational error but I keep getting $\frac{81}{5}$ .
November 8th 2008, 10:09 AM
galactus

$\int_{0}^{1}\int_{2y^{2}}^{4-2y}(-x-2y+4)dxdy$

$\int_{0}^{1}\int_{2y^{2}}^{4-2y}\int_{0}^{-x-2y+4}dzdxdy$

Now, try doing it by switching the limits of integration.
November 8th 2008, 10:11 AM
Mathstud28

Quote:

Originally Posted by galactus

$\int_{0}^{1}\int_{2y^{2}}^{4-2y}(-x-2y+4)dxdy$

$\int_{0}^{1}\int_{2y^{2}}^{4-2y}\int_{0}^{-x-2y+4}dzdxdy$

Now, try doing it by switching the limits of integration.

Ahh thank you very much Galctus! I had $\int_{-2}^{1}\cdots$ for some reason haha

EDIT: I see what I did, I solved the inequality wrong by mistake. It's good now.
November 8th 2008, 11:32 AM
Apprentice123

thank you very much
November 10th 2008, 02:37 AM
Apprentice123

There is a "tutorial" to build the graphic.
November 12th 2008, 02:27 PM
Apprentice123

Quote:

Originally Posted by Mathstud28

Ahh thank you very much Galctus! I had $\int_{-2}^{1}\cdots$ for some reason haha

EDIT: I see what I did, I solved the inequality wrong by mistake. It's good now.

$2y^2=x$ A parable

$\frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1$ What is this graphic?
November 12th 2008, 02:37 PM
Mathstud28

Quote:

Originally Posted by Apprentice123

$2y^2=x$ A parable

$\frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1$ What is this graphic?

If I am understanding you correctly, a plane.
November 12th 2008, 02:47 PM
Apprentice123

Quote:

Originally Posted by Mathstud28

If I am understanding you correctly, a plane.

Thank you. Why the integral range from 0 to 1?
November 23rd 2008, 10:47 AM
Apprentice123

Why not?

$\int_{0}^{2} \int_{2y^2}^{4-2y} \int_{0}^{4-x-2y}dzdxdy$

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