Integrate $f(x,y,z) = x^2 + y^2$ over the prism shown
My problem isn't the integration process but just to determine what the limits are.
$$\int_0^4 \int_{0}^{1-x} \int x^2 + y^2 dzdydx $$
I think those two limits may be correct but I don't know how to get the third, I understand how to find limits form a shape like a tetrahedron but a bit confused and my notes don't help me with this shape.
Best Answer
Notice the plane that bounds that prism is given by
$$ z +y = 1 $$
Hence, your limits of integration goes from $0$ to $1 - y$.