# Calculate volume

• Nov 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 $y=0$

$\frac{17}{5}$
• Nov 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 $y=0$

$\frac{17}{5}$

Maybe I am making a computational error but I keep getting $\frac{81}{5}$.
• Nov 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.
• Nov 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.
• Nov 8th 2008, 11:32 AM
Apprentice123
thank you very much
• Nov 10th 2008, 02:37 AM
Apprentice123
There is a "tutorial" to build the graphic.
• Nov 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?
• Nov 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.
• Nov 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?
• Nov 23rd 2008, 10:47 AM
Apprentice123
Why not?

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