Question

need help sketching a region of integration and re-expressing the bounds in dxdydz and dydxdz. problem attached

Answer 1

You integrate "from inside out", so you first look at the z-coordinate, then y, then x. (Hence dz dy dx) . So you know that z is between x and 1, y is between 1-x and 1, x is between 0 and 1.

a) Start with x, then draw y , then z.
b) + c) you can intgegrate in whatever order you want, as long as you remember to use the right integral borders.

Note that in the end, you want to get a number (in most cases) not a function.

Answer 2

Yeah ive been trying to do that but I am having a hard time making a 3d image out of all of it

Answer 3

Ok do the following: first draw a x-y plane. Then draw the line y=-x+1. Then look at the xz-Plane and again, draw the line z= x. Combine them together and it should look like a pyramid with the Points(x,y,z): (1,0,1) , (0,1,0) , (1,0,0)

Correct me if im wrong, im not 100% sure either.