0
$\begingroup$
  • Evaluate the integral $\int_{E} f$ where $f(x, y, z)=x y+z$ and $E$ is the tetrahedron in $\mathbb{R}^{3}$ with vertices $(0,0,0),(1,0,0),(0,1,0)$ and $(0,0,1).$ Use Fubini's theorem

My Attempt.

enter image description here

Note that $\{(x,y,z): 0\leq x+y+z\leq 1\}$, then $\{0\leq x\leq 1, 0\leq y\leq 1-x, 0\leq z<1-x-y\}$.

May you check my attemp, and may you write boundeds of integrals?

$\endgroup$
1
  • $\begingroup$ Would you like to attempt to write the integral as written? I think your inequalities work. $\endgroup$ – Ninad Munshi Dec 23 '19 at 9:21
0
$\begingroup$

What you have written is correct. The integral is $\int_0^{1}\int_0^{1-x}\int_0^{1-x-y} (xy+z) dzdydx$.

$\endgroup$
1
  • $\begingroup$ Thanks for answer $\endgroup$ – user295645 Dec 23 '19 at 9:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy