# Double integration

• Jul 23rd 2007, 04:19 PM
kittycat
Double integration
Use double integration to find the volume of the solid that is common to the cylinders x^2 + y^2 =25 and x^2 + z^2 = 25.

Thank you very much.
• Jul 23rd 2007, 04:47 PM
galactus
You could find the volume of one octant and then multiply by 8.

$8\int_{0}^{5}\int_{0}^{\sqrt{25-x^{2}}}\sqrt{25-x^{2}}dydx$

= $8\int_{0}^{5}(25-x^{2})dx$
• Jul 23rd 2007, 05:07 PM
kittycat
Hi galactus,

thank you very much for your reply. Why multiple by 8? Could you please explain to me? Thanks.
• Jul 23rd 2007, 06:32 PM
ThePerfectHacker
Quote:

Originally Posted by kittycat
Hi galactus,

thank you very much for your reply. Why multiple by 8? Could you please explain to me? Thanks.

He used symmetry.

The shape was equally divided into the 8 octants. He chose only 1 octant and multiplied it by 8.
• Jul 24th 2007, 06:55 AM
curvature
Quote:

Originally Posted by ThePerfectHacker
He used symmetry.

The shape was equally divided into the 8 octants. He chose only 1 octant and multiplied it by 8.

Yes. See the graph below.