Question

Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 2.

Answer 1

\[\int\limits_{x=0}^{2}\int\limits_{y=0}^{2-x}\int\limits_{z=0}^{2-x-y}dx dy dz=\int\limits_{x=0}^{2}\int\limits_{y=0}^{2-x}(2-x-y)dxdy\]=\[\int\limits_{x=0}^{2}((2-x)(2-x)-(2-x)^{2}/2)dx=\int\limits_{x=0}^{2}(2-x)^{2}dx/2\]=4/3

Answer 2

i knew itd be multi integraled lol

Answer 3

i knew itd be multi integraled lol

Answer 4

good job :)