To Shade the Area Between $x^2$ and $\sqrt{x}$

by caffeinemachine   Last Updated June 23, 2018 14:23 PM

I want to draw the following image in tikZ

enter image description here

Basically I want to draw the boundary of the unit square, plot the x^2 and \sqrt x functions, and shade the area between them.

In my attempt to draw the two curves, I tried this


  \begin{axis}[axis lines=middle,]
  \addplot[name path=F,black,domain={0:5}] {sqrt x};
  \addplot[name path=G,black,domain={0:5}] {x^2};

But the output I am getting is

enter image description here

Somehow the \sqrt{x} function is getting flattened out.

Also, how to get rid of the arrows I have in the axes and make an enclosing box like I have in the hand-drawn picture.

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