Question

Set up a triple integral for the volume of the solid enclosed by the planes x = 0, y = 0, z = 0 and x + y + z = 2.​

Answer 1

`\displaystyle \int_0^2 \int_0^(2-x) \int_0^(2-x-y) dz \, dy \, dx = \int_0^2 \int_0^(2-x) (2-x-y) \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^2 (x-2)^2 \, dx = \boxed{\frac43}`