# Another Triple Integral Question

1. Apr 10, 2004

### Theelectricchild

Hello.

Here is the original question http://

My difficuly is understanding the limits of integration--- party due to how the solid in question is "sliced" by those planes. I know how to visualize the parabolic cylinder, but I need help on 1. limits on integration, and 2. Order of integration.

I doubt I would have to use polar coordinates since the region in question has no square roots...

Thanks for you help I really do appreciate this.

Last edited by a moderator: Apr 20, 2017
2. Apr 10, 2004

### Theelectricchild

Arghh that links not working, just copy paste it into the url. Sorry.

3. Apr 10, 2004

### outandbeyond2004

TEChild, you can use Latex coding here, click on this link:

$$\int \int \int_E (x + 2y)dV$$

where E is bound by the parabolic cylinder

$$y=x^2$$

and the planes

$$x=z,x=y,z=0$$

Last edited: Apr 10, 2004
4. Apr 10, 2004

### outandbeyond2004

Divide and conquer. z appears as an independent variable once and as a constant. So, easy to eliminate x:

$$\int _E ()dV = \int_0^1 dz \int dy \int_z^1 ()dx$$

Do you see why the upper limit on z is 1? Solve the innermost integral as tho y and z were constants.

5. Apr 10, 2004

### Theelectricchild

actually I dont see why the upper limit on z is one... thats where I was confused --- I understand why it starts at 0 of course... and also the y limits are giving me trouble...

6. Apr 11, 2004

### outandbeyond2004

taking z as the independent variable, ask yourself: what is the greatest z value a point in the bounded volume can have?

7. Apr 11, 2004

### Theelectricchild

ahhhh i got it thanks so much

8. Apr 11, 2004

### Divergent13

Ooh Bellingham--- are you a graduate student at Western Washington U. outandbeyond?