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


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


/* [wxMaxima: comment start ]
Priklad 4.5.
   [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 ] */
derexpr2:diff(expr2,t);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
lenght:'integrate(sqrt((derexpr1^2)+(derexpr2^2)),t,0,2*%pi);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
trigsimp(radcan(lenght));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sub:4*3*a*'integrate(cos(t)*sin(t),t,0,%pi/2);
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: comment start ]
Priklad 4.6.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
f:log(cos(x));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
derf:diff(f,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
lenght:'integrate(sqrt(1+derf^2),x,0,a);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(cos(x)>0)$ radcan(lenght);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
trigsimp(%);
/* [wxMaxima: input   end   ] */


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


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


/* [wxMaxima: comment start ]
Priklad 4.7.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
f:x^2/a*sqrt(1-x^2/a^2);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
a:3$ plot2d([f,-f],[x,-5,5],[y,-5,5]);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
kill(a);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
Va:%pi*'integrate(f^2,x,-a,a);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
Vb:2*%pi*'integrate(expand(f^2),x,0,a);
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: comment start ]
Priklad 4.8.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
f:tan(x)/x;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
V:2*%pi*'integrate(x*f,x,%pi/4,%pi/3);
/* [wxMaxima: input   end   ] */


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



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