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


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


/* [wxMaxima: comment start ]
Priklad 4.9.
   [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,sin(t)>0)$ V:%pi*'integrate(expr2^2*abs(derexpr1),t,0,%pi);
/* [wxMaxima: input   end   ] */


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


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


/* [wxMaxima: comment start ]
Priklad 4.10.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
expr1:a*((t^2-3)/(t^2+1));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
expr2:a*((t*(t^2-3))/(t^2+1));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
a:1$ plot2d([parametric,expr1,expr2,[t,-3,3]]); kill(a)$
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: input   start ] */
V:2*%pi*'integrate(expr2*expr1*abs(derexpr1),t,-sqrt(3),sqrt(3));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(t>0,a>0)$ iresult:factor(V);
/* [wxMaxima: input   end   ] */


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


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


/* [wxMaxima: comment start ]
Priklad 4.11.
   [wxMaxima: comment end   ] */


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


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


/* [wxMaxima: input   start ] */
derf2:subst(1/cos(x),sec(x),derf);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
Q:2*%pi*'integrate(f*sqrt(1+derf2^2),x,0,%pi/4);
/* [wxMaxima: input   end   ] */


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


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


/* [wxMaxima: input   start ] */
subst([asinh(1)=log(1+sqrt((1^2)+1)),asinh(1/2)=log((1/2)+sqrt((1/2)^2+1))],%);
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: comment start ]
Priklad 4.12.
   [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 ] */
Q:2*%pi*'integrate(expr2*sqrt(derexpr1^2+derexpr2^2),t,0,%pi);
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: input   start ] */
iresult:2*6*%pi*a^2*'integrate(cos(t)*sin(t)^4,t,0,%pi/2);
/* [wxMaxima: input   end   ] */


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



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