Question

WILL MEDAL
set up all six possible triple integrals of the tetrahedron enclosed by the coordinate planes and the plane x + 2y + 3z = 30

Answer 1

\[\int\limits\limits_{0}^{15} \int\limits\limits_{0}^{(2/3)y + 10} \int\limits\limits_{0}^{(z-10)/3} dx dz dy\]

Answer 2

\[\int\limits\limits_{0}^{10} \int\limits\limits_{0}^{3z + 15} \int\limits\limits_{0}^{2y -30} dx dy dz\]

Answer 3

\[\int\limits\limits_{0}^{30} \int\limits\limits_{0}^{1/2(x) +15} \int\limits\limits_{0}^{2/3 (y) + 10} dz dy dx\]

Answer 4

check three please

Answer 5

@xapproachesinfinity

Answer 6

I forgot how to do this stuff from calc3
you will need a person who is good acquainted to this

Answer 7

i had some ideas here and there but not really helping
@zepdrix could help :)

Answer 8

@ganeshie8

Answer 9

hey @ganeshie8 how are you doing
been awhile, nice to see you here again :)

Answer 10

@amistre64

Answer 11

Instead set up the traces, and work from them

Answer 12

i just used projections

Answer 13

I mean you can do xy, xz, yz plane and work from there

Answer 14

can you elaborate on that.

Answer 15

hey @xapproachesinfinity :)

Answer 16

Say you can let z = 0, and then you have

Answer 17

But it will be more useful if you draw it on your original drawing, that way you're slicing it in planes, and can set up your integrals.

Answer 18

take slices of those