- #1

Dx

how do i solve for this, can someone get me started halfway, plz?

Dx

- Thread starter Dx
- Start date

- #1

Dx

how do i solve for this, can someone get me started halfway, plz?

Dx

- #2

- 17

- 0

I dont know if you have solved this problem already, but here goes:

The first step you will want to do is draw two diagrams, one of the solid, and one projection of it on the x-y plane.

Then solve the equation for z (or x or y whichever is going to produce the easiest integral outcome).

In this case I would go for the z solution:

z=2x+3y-6

Then determine the axis intersections in order to find the integral limits.

Set up your triple integral, solve.

The first step you will want to do is draw two diagrams, one of the solid, and one projection of it on the x-y plane.

Then solve the equation for z (or x or y whichever is going to produce the easiest integral outcome).

In this case I would go for the z solution:

z=2x+3y-6

Then determine the axis intersections in order to find the integral limits.

Set up your triple integral, solve.

Last edited:

- #3

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

"projecting" down to the x,y plane (z= 0) gives the line where the plane 2x+ 3y+ z= 6 crosses the x,y plane: 2x+ 3y= 6. We need to integrate over the triangle with edges x=0, y=0, 2x+ 3y= 6.

Solving for y, y= 2- (2/3)x. The second integral will be with respect to y (dy) and will have limits y= 0 and y= 2-(2/3)x.

Finally, project to the x-axis itself. The line 2x+3y= 6 crosses the x-axis when y= 0: 2x= 6 or x= 3. The final integral will be with respect to x (dx) and will have limits x= 0, x= 3.

The triple integral you want is

integral (x=0 to 3) integral (y=0 t0 2-(2/3)x) integral (z= 0 to 6- 2x+3y)(2x+3y)dzdydx.

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 4K

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 5K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 639

- Last Post

- Replies
- 2

- Views
- 749