Question

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?

Answer 1

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

Answer 2

\[\int\limits_{0}^{3}\int\limits_{0}^{8}8dxdy\]

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)

Answer 3

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.

Answer 4

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

Answer 5

Have you gotten to triple integrals yet chag?

Answer 6

No. Haven't got to triples yet.

Answer 7

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!
\[\int\limits_{0}^{z} \int\limits_{0}^{y} \int\limits_{0}^{x} f(x,y,z) dx dy dz\]

Answer 8

Great. You're invited to my next soiree.

Answer 9

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

Answer 10

I think they slipped in 3 ft and 8 inches

Answer 11

Z is 36 because the 3 is in units feet.

Answer 12

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