Kirish bob. Trapetsiyalar formulasi

> restart; r>0:
> f:=x->sqrt(r^2-x^2);
> dif1:=diff(f(x),x);
> L:=int(sqrt(1+dif1^2),x=0..r);

> Mx:=int(f(x)*sqrt(1+dif1^2),x=0..r);
Warning, unable to determine if -r is between 0 and r; try to use assumptions or set _EnvAllSolutions to true

> My:=int(x*sqrt(1+dif1^2),x=0..r);
> xc:=My/L; yc:=Mx/L;

> r:=2:xc;yc;
36-misol. x=a(t–sint), y=a(1–cost)(a>0) sikloida bitta arkining (0t2) uzunligini og`irlik markazining koordinanalarini hisoblang (14- rasm).
Yechish.
1)Egri chiziq grafigi:
> with(plots):
> plot([1*(t-sin(t)), 1*(1-cos(t)), t=0..2*Pi]);

2) yoy uzunligini hisoblaymiz:
x`=a(1-cost), y`=asint


=
3) ,

37-misol. Qutb koordinatalar tekisligida berilgan =a(1+cos) kordioida (16-rasm) yoyi bo`lagining og`irlik markazining koordinatalarini hisoblang.
Yechish:
kordioida bo`lagining massasi



Oy o`qqa nisbatan statik momenti:



=

Ox o`qqa nisbatan statik momenti:





> restart;
> with(plots):with(Student[Calculus1]):
> plot([2*(1+cos(t)),t,t=0..2*Pi],coords=polar,thickness=2);



> restart;with(plots):with(Student[Calculus1]):
Warning, the name changecoords has been redefined
> r:=t->a*(1+cos(t));
> My:=Int(r(t)*cos(t)*2*a*cos(t/2),t=0..Pi);