Question

Volume between two surfaces using a double integral.

Answer 1

You can has a medal for this.

Answer 2

hmm. this is a cool problem. They intersect at
\[\cos (|x|+|y|) = \sin (|x|+|y|) = \sqrt 2 / 2\]
so you'd integrate z1 from 0 to sqrt 2 / 2

and z2 from sqrt 2 / 2 to 1. Hmmm....

Answer 3

Thanks for the clue @AllTehMaffs

Answer 4

dunno how much it helps. Just mah brainz trying to think through this ^_^

Answer 5

I have a feeling converting to polar coordinates could be helpful, but I am not certain.

Answer 6

Any ideas how to solve this one @hartnn?

Answer 7

I got an idea

Answer 8

I watched a video of someone solving a problem similar to this, and they found the 2-d "image" of the shadow of the solid.

Answer 9

If there is a flashlight above the solid shining straight down onto the xy plane, then there will be a shadow that is like a diamond with vertices (pi/2,0), (0, pi/2), (-pi/2, 0), and (0,-pi/2)

Answer 10

like this ? http://www.wolframalpha.com/input/?i=z+%3D+cos%28 |x|%2B|y|%29+ the contour plot

Answer 11

Yes!!!

Answer 12

Interesting, I also get the feeling that this thing has 4-fold symmetry.

Answer 13

yeah, if you can find a slice of this, you can def. just multply it . Just don't know which surface boundaries to use!! :P

Answer 14

Perhaps if we find a quarter of its volume in the first quadrant of the xy plane. Let x=0, y=0, and y = -x + pi/2.

Answer 15

Then we are working with a triangle.

Answer 16

I am brushing my teeth, brb.