Limits of a Triple Integral

The question I am trying to work out states that a TETRAHEDRON, $\displaystyle T$, is bounded by the planes $\displaystyle x=2$, $\displaystyle y=0$, $\displaystyle z=0$ and $\displaystyle 3x-6y-2z=0$.

The triple integral is given as: $\displaystyle \int\int\int_{T} x dv$

I am have an extremely tough time in trying to visualize and draw the region, also determining the limits of each of the integral.

I think the innermost limit for $\displaystyle dz$ would be $\displaystyle 0\leq z \leq \frac{3}{2}x - 3y$ but the others have me stumped.

Help anyone?

Tammy

2 Attachment(s)

Re: Limits of a Triple Integral

Attachment 28236

See the attached figures and try to visualize the limits....

Attachment 28235

Re: Limits of a Triple Integral

Thank you for the images. Now I do can visualise the planes.

But I am really sorry to be so dense but how do I determine the limits for dy and dx.

Do I need to work out where the planes intersect? I am really struggling to understand this.