restart;
f:=cosh(t);
g:=sinh(t);
df:=diff(f,t);
dg:=diff(g,t);
Int(sqrt(df^2+dg^2),t=0..b);
b:=arcsinh(4/3);
L:=int(sqrt(df^2+dg^2),t=0..b);
?EllipticK
evalf(L);
Digits:=20;
evalf(L);
plot([f(t),g(t),t=0..b]);
f:=erf(t);
g:=InverseJacobiAM(t,1);
plot([f,g,t=0..1]);
df:=diff(f,t);
dg:=diff(g,t);
L:=int(sqrt(df^2+dg^2),t=0..1);
evalf(L);