Finding limits and order of integration for a triple integral

[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.

 

[Theelectricchild]

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

 

[outandbeyond2004]

TEChild, you can use Latex coding here, click on this link:
https://www.physicsforums.com/showthread.php?t=8997

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

where E is bound by the parabolic cylinder

$$y=x^2$$

and the planes

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

 

[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.

 

[Theelectricchild]

actually I don't see why the upper limit on z is one... that's where I was confused --- I understand why it starts at 0 of course... and also the y limits are giving me trouble...

 

[outandbeyond2004]

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

 

[Theelectricchild]

ahhhh i got it thanks so much

 

[Divergent13]

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