Question

find the volume of the solid bounded by plane z=x, y=x, x+y=z, z=0

Answer 1

how would i set this up?

Answer 2

by getting the right picture :) still trying to hash it out tho

Answer 3

z=x+y

Answer 4

z=0 is a x-y plane
x=z is a plane passing through y-axis and equal distance from both x and z axis
y=z goes the similar above

Answer 5

include z=x

Answer 6

and x=y

Answer 7

0<z<1
0<x<1
0<y<1/2

are the limts for integration it i see them correctly

Answer 8

how'd you get the 1/2 for y?

Answer 9

the intersection in the xy plane of z=x+y and x=y is what i think i see there

Answer 10

okay so 2y=z so y=1/2?

Answer 11

yep

Answer 12

okay I'm good so far!

Answer 13

there is a plane that needs to be defined as our "cap" in order to integrate these limits under

Answer 14

x+y=z?

Answer 15

i believe it is created by the points:

(0,1,0) , (1,0,1), and (1/2,1/2,0)