Sketch the integration area

Question

I have a trippel integral with bounderies $z<x<y+z$, $0<y<1$, $1+y<z<2y$.

I have done the calculations but I am supposed to sketch the integration area in three dimensions. How can I do this by hand? ( how to type in mathematica is also off interest )

Thanks!

Answer 1

By hypothesis,

$(0<y<1)\; \land \; (y<z<2y )\implies$

$ 0<z<2$.

and

$(0<y<1) \; \land \; (z<x<y+z) \implies$

$ 0<x<3$.

So, the integral is

$$\int_0^3\int_0^1\int_0^2 dxdydz=$$

$$(3-0)(1-0)(2-0)=6.$$