Plotting, Integrating two variable function with cross-restricted domain

Hello, I have two problems.

the first is plotting 3D function, the domain is "0<x<y<1". (I could find examples like integrating function with domain 0<x<1, 0<y<1, but I could not find examples for a<x<y<b.)

the second is just Intergrating the funcntion below.

For the plot you can use RegionFunction, which takes a pure function which takes x, y, and z values::

Plot3D[1/(1-x),{x,0,1},{y,0,1},RegionFunction->Function[{x,y,z},x<y]]


Your second issue is fixed by spelling Integrate properly (notice that Intergrate is in blue, meaning that it is an undefined global variable), and by swapping the order of integration:

Integrate[Sqrt[x^2+y^2]/Pi, {x, 0, 1}, {y, -Sqrt[1-x^2], Sqrt[1-x^2]}]


1/3

• Also, Plot3D[1/(1 - x), {x, 0, 1}, {y, x, 1}] May 26 at 0:05
• Wow... I had so many mistakes, really really thanks. May 26 at 2:25