Volume of Double Integral: Finding the Region with Graphed Equations

[stolencookie]

Homework Statement

z=x^2+xy ,y=3x-x^2,y=x find the volume of the region

Homework Equations

The Attempt at a Solution

I graphed y=3x-x^2 and y=x I am confused on which region I use to find the volume. Do I use the upper region or the lower region.

 

[berkeman]

Homework Statement

z=x^2+xy ,y=3x-x^2,y=x find the volume of the region

Homework Equations

The Attempt at a Solution

I graphed y=3x-x^2 and y=x I am confused on which region I use to find the volume. Do I use the upper region or the lower region.

Doesn't the question give 3 equations as constraints for the volume enclosed? Can you do a 3-D graph of all 3 equations?

 

[stolencookie]

Doesn't the question give 3 equations as constraints for the volume enclosed? Can you do a 3-D graph of all 3 equations?

Can't do a 3D graph the two constraints are y=x and y=3x-x^2 , I use the z=x^2+xy to find the volume using the double integrals just having trouble with the set up.

 

[LCKurtz]

Homework Statement

z=x^2+xy ,y=3x-x^2,y=x find the volume of the region

Homework Equations

The Attempt at a Solution

I graphed y=3x-x^2 and y=x I am confused on which region I use to find the volume. Do I use the upper region or the lower region.

I would assume you want the upper region. The lower region has a boundary portion of $y=0$ which is not mentioned in the problem.

 

[Ray Vickson]

Homework Statement

z=x^2+xy ,y=3x-x^2,y=x find the volume of the region

Homework Equations

The Attempt at a Solution

I graphed y=3x-x^2 and y=x I am confused on which region I use to find the volume. Do I use the upper region or the lower region.

In your (x,y)-space there are four regions between the blue and red curves: (i) the south-west region, in which x and y can both go to -∞; (ii) the southern region, in which x can go to ±∞ but y can just go to -∞; (iii) the north-west region, in which x and y can go to +∞; and (iv) the north region, in which x and y are both bounded. Regions (i)--(iii) have infinite areas, which will lead to infinite volumes when we add a third dimension; only region (iv) gives a finite answer.