File:Quaplot.jpg

$y=\,$qua$(x)=\frac{1}{2}\big( x\sqrt{1\!-\!x^2}+\arcsin(x)\big)$

The additional horizontal grid line corresponds to $y=\,$qua$(1)=\pi/4\approx 0.785398$

C++ generator of curve
ado.cin should be loaded in order to compile the code below

//#define DB double
 * 1) include
 * 2) include
 * 3) include
 * 1) define DB double
 * 2) define DO(x,y) for(x=0;x<y;x++)
 * 3) include"ado.cin"

DB qua(DB x){ return .5*( x*sqrt(1.-x*x) + asin(x));}

int main{ int m,n; DB x,y; FILE *o; o=fopen("quaplo.eps","w"); ado(o,1004,804); fprintf(o,"2 2 translate 1000 1000 scale\n"); DO(m,11){ M(.1*m,0) L(.1*m,.8)} DO(n,9) { M(0,.1*n) L(1,.1*n)} fprintf(o,"2 setlinecap 1 setlinejoin .002 W S\n"); M(0,M_PI/4.) L(1,M_PI/4.) fprintf(o," .001 W S\n"); DO(m,101){x=.01*m;y=qua(x); if(m==0)M(x,y) else L(x,y) } fprintf(o,"1 0 0 RGB .003 W S\n"); fprintf(o,"showpage\n%c%cTrailer\n",'%','%');fclose(o); system("epstopdf quaplo.eps"); system(   "open quaplo.pdf"); }
 * 1) define M(x,y) fprintf(o,"%6.5lf %6.5lf M\n",0.+x, 0.+y);
 * 2) define L(x,y) fprintf(o,"%6.5lf %6.5lf L\n",0.+x, 0.+y);

Latex generator of labels
\documentclass[12pt]{article} \usepackage{geometry} \paperwidth 1010pt \paperheight 810pt \topmargin -104pt \oddsidemargin -72pt \pagestyle{empty} \usepackage{graphicx} \parindent 0pt \textwidth 1200px \textheight 900px \newcommand \sx {\scalebox} \begin{document} \begin{picture}(1008,804) \put(0,0){\includegraphics{quaplo}} \put(14,744){\sx{4.2}{$y\!=\!\mathrm{qua}(x)$}} \put(9,590){\sx{4}{$0.6$}} \put(9,390){\sx{4}{$0.4$}} \put(9,190){\sx{4}{$0.2$}} \put(170,8){\sx{4}{$0.2$}} \put(370,8){\sx{4}{$0.4$}} \put(570,8){\sx{4}{$0.6$}} \put(770,8){\sx{4}{$0.8$}} \put(980,8){\sx{4}{$x$}} \end{picture} \end{document}