Question

use double integral to find volume of tetrahedron bounded by the cooridnate planes and the plane
5x+5y+2z=10

Answer 1

i'm down to do this whole thing step by step.

first thing: do you know how to graph the plane?

Answer 2

Lol yeah I was about to say that I think what would help the best is to first graph the picture

Answer 3

I can do the int without much issue i need a little direction setting up the problem.

Answer 4

Euler seems to be more confident about teaching you it so I will let him expain it to you since I'm actually studying to take a final for this in calc 3 and although this would be good review, I think you definitely want someone who can easily explain it to you

Answer 5

you need to graph the boundaries to know the limits of the integrals, which in this case is a plane.

do you know how to graph this plane?

Answer 6

thats where i am a bit fuzzy.

Answer 7

to graph a plane, all you need to do is find the intercepts.

similarly to 2 dimensions, where finding x-intercepts are when y = 0, in 3-d, the x-intercepts are when both y and z = 0.

when y = z = 0 --> 5x = 10 . the x-intercept of the plane is x = 2
when x = y = 0 --> 2z = 10. the z-intercept of the plane is z = 5
y intercept = 2

here is the graph:



it's the tetrahedron between origin and the plane. the x-y plane looks like this:

Answer 8

so the integrating limits of x are from x = 0 to x = 2 and the integrating limits of y are from y = 0 to y = 2 - x

Answer 9

now i feel like a idiot....one should never start homework so late at night.

Answer 10

the function you are integrating is f(x,y) = z = 1/2(5x + 5y)

\[1/2 \int\limits_{0}^{2}\int\limits_{0}^{2-x} (10 - 5x - 5y) dy dx\]

Answer 11

CORRECTION: the function you are integrating is f(x,y) = z = 1/2(10 - 5x - 5y)