Question

Let E be the solid region in the first octant that is bounded by the planes x=2, y=0, z=0, and z=x. Evaluate [triple integral] xdV

Answer 1

there's no other bound on y ?

Answer 2

yess, sorry y=x

Answer 3

then the bounds are 0<=y<=x, 0<=z<=x, 0<=x<=2
make sense?

Answer 4

Yup.

Answer 5

Is there a specific order that I would integrate in? e.g dV =dydxdz or dV =dzdydx or dV =dxdydz?

Answer 6

x is the only one that we have as bound by a constant, so we have to do dx last or else we won't get a numerical answer
the order of dy and dz do not matter here

Answer 7

Fantastic! Thank you very much :)

Answer 8

welcome!