restart;
f:=2*sin(y);
dfdy:=diff(f,y);
L:=int(sqrt(dfdy^2+1),y=Pi/6..5*Pi/6);
evalf(L);




restart;
f:=x^(1/3)+4*x^(2/3);
dfdx:=diff(f,x);
L:=int(sqrt(dfdx^2+1),x=0..1);
evalf(L);




restart;
f:=tan(x);
dfdx:=diff(f,x);
A:=2*Pi*Int(f*sqrt(dfdx^2+1),x=Pi/5..7*Pi/16);
evalf(A);




restart;
f:=int(4*sin(t),t=0..y);
dfdy:=diff(f,y);
A:=2*Pi*int(f*sqrt(dfdy^2+1),y=0..Pi/4);
evalf(A);