I need to integrate x over the region bounded by x=1, y=1, z=1 and x+y+z=2. I am just wondering if the following limits are correct:
1 < z < 2-x-y
1 < y < 3-x
1 < x < 2
I get an answer of -9/8 so I'm assuming that's not right.
I need to integrate x over the region bounded by x=1, y=1, z=1 and x+y+z=2. I am just wondering if the following limits are correct:
1 < z < 2-x-y
1 < y < 3-x
1 < x < 2
I get an answer of -9/8 so I'm assuming that's not right.
It's been a while but I think the limits are as follows:
$\displaystyle 1\leq z\leq 2-x-y$
$\displaystyle 1-x\leq y \leq 1$
$\displaystyle 0 \leq x \leq 1$
See once we have the limits for z, we can plug z=1 into our equation, solve for y and plot $\displaystyle y=1, x=1, y=1-x$ in the $\displaystyle xy$ plane and see the region clearly to determine the limits for x and y
So we get $\displaystyle y=1-x$ and when we plot it we can see that its the lower limit for y
Alright if you reverse my top and bottom limits on z then I think we're good. We both made the mistake of assuming that the region of integration was bounded above by the plane given by x+y+z=2, but that plane is actually the bottom of the region