## anonymous 5 years ago Solve kjackson's problem by double integrals. A rectangular prism planter is filled with potting soil. It has a length of 3 feet and a width of 8inches and a height of 8 inches. How much potting soil can it hold?

1. anonymous

Alright, I prefer doing these with triples, but it was good to think about these again. integral(from 0 36) integral(0 8) (8dA) integral(from 0 36) 8x|(0 to 8) integral(from 0 36) 64dz 64z|(0 36) 2034

2. anonymous

$\int\limits_{0}^{3}\int\limits_{0}^{8}8dxdy$ The outer integral would be the length (or y) and the inner one would be width(or x) and the inside is 8 because the height (z) is 8 it would just simplify to 8 * 3 * 3 (which is the volume equation)

3. anonymous

Except 3 would be 36, otherwise proper. Do you see why I prefer triples though? It seems more logical, but perhaps thats just me. Same thing is being accomplished, just with triples I see where its coming from.

4. anonymous

Great, I was trying to figure out what f(x,y) would be. Now I know.

5. anonymous

Have you gotten to triple integrals yet chag?

6. anonymous

No. Haven't got to triples yet.

7. anonymous

Ok, well they are the same idea. Its just it seems clearer to do volume problem in them: In this problem z = 36, y = 8, x = 8. Just makes more sense to me, but I also like using overkill math techniques to figure out simple stuff like this like you do. I am very fun at parties! $\int\limits_{0}^{z} \int\limits_{0}^{y} \int\limits_{0}^{x} f(x,y,z) dx dy dz$

8. anonymous

Great. You're invited to my next soiree.

9. anonymous

I don't understand why z is 36..... z is just the height of the box, which is 8 the triple integral would just be $\int\limits_{0}^{3}\int\limits_{0}^{8}\int\limits_{0}^{8}1dzdydx$ again, giving you 8 * 8 * 3 = 192

10. anonymous

I think they slipped in 3 ft and 8 inches

11. anonymous

Z is 36 because the 3 is in units feet.

12. anonymous

oops i didn't see that i have people that mix units :x i stand corrected! scot's right