Question

find volume of the tetrahedron formed by x+y+z=1 using double integrals.

Answer 1

\[\int\limits_{0}^{1}\int\limits_{0}^{1-x}(1-x-y)dydx\]

Answer 2

i get 1/3 can u confm

Answer 3

1/6

Answer 4

I don't know how u get 1/6

Answer 5

did you evaluate the dx integral at 0?

Answer 6

do you see where you made your mistake?

Answer 7

no

Answer 8

\[\left.x-x^2+\frac{x^3}{3}+\frac{(1-x)^3}{6}\right|_{0}^{1}\]
\[=\left(1-1^2+\frac{1^3}{3}+\frac{(1-1)^3}{6}\right)-\left(0-0^2+\frac{0^3}{3}+\frac{(1-0)^3}{6}\right)\]

\[=1-1+\frac{1}{3}+0-0+0-0-\frac{1}{6}=\frac{1}{3}-\frac{1}{6}=\frac{1}{6}\]