/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 17.10.1 ] */
/* [wxMaxima: title   start ]
Priklady - kapitola 4 - a
   [wxMaxima: title   end   ] */


/* [wxMaxima: comment start ]
Cisla prikladu koresponduji s diplomovou praci
   [wxMaxima: comment end   ] */


/* [wxMaxima: comment start ]
Priklad 4.1.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate(sin(x),x,0,%pi);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ev(%,nouns);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
f(x):=sin(x); g(x):=0;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
draw2d(grid=true,xaxis=true,yaxis=true,xrange=[-1,7],yrange=[-1.5,1.5],fill_color=grey,filled_func=true,filled_func=f(x),explicit(g(x),x,0,%pi),filled_func=false,color=black,key="sin(x)",explicit(f(x),x,0,2*%pi),color=red,key="x",explicit(g(x),x,-1,7));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 4.2.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate(abs(cos(x)),x,0,2*%pi);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
'integrate(cos(x),x,0,%pi/2)-'integrate(cos(x),x,%pi/2,3*%pi/2)+'integrate(cos(x),x,3*%pi/2,2*%pi);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ev(%,nouns);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
f(x):=cos(x); g(x):=0;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
draw2d(grid=true,xaxis=true,yaxis=true,xrange=[-1,7],yrange=[-1.5,1.5],fill_color=grey,filled_func=true,filled_func=f(x),explicit(g(x),x,0,2*%pi),filled_func=false,color=black,key="cos(x)",explicit(f(x),x,0,2*%pi),color=red,key="x",explicit(g(x),x,-1,7));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 4.3.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
f(x):=x^2; g(x):=2-x;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
draw2d(grid=true,xaxis=true,yaxis=true,xrange=[-4,4],yrange=[-2,7],fill_color=grey,color=black,key="x^2",explicit(f(x),x,-2.4,2.4),color=red,key="2-x",explicit(g(x),x,-3,3));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
solve(f(x)=g(x),x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
'integrate(g(x)-f(x),x,-2,1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ev(%,nouns);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
draw2d(grid=true,xaxis=true,yaxis=true,xrange=[-4,4],yrange=[-2,7],filled_func=true,filled_func=f(x),explicit(g(x),x,-2,1),filled_func=false,fill_color=grey,color=black,key="x^2",explicit(f(x),x,-2.4,2.4),color=red,key="2-x",explicit(g(x),x,-3,3));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 4.4.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
expr1:a*cos(t)^3;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
expr2:a*sin(t)^3;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
derexpr1:diff(expr1,t);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(a>0)$ assume(sin(t)>0)$ absderexpr1:abs(derexpr1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
Int:'integrate(absderexpr1*expr2,t,0,2*%pi);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ev(Int,nouns);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
forget(a>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
forget(sin(t)>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
plot2d([parametric, 1*cos(t)^3, 1*sin(t)^3, [t,0,2*%pi]]);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */

/* [wxMaxima: input   end   ] */



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