Length of an arc : arcLen

### 4.17.2 Length of an arc : arcLen

arcLen takes four arguments : an expression ex (resp. a list of two expressions [ex1,ex2]), the name of a parameter and two values a and b of this parameter.
arcLen computes the length of the curve define by the equation y=f(x)=ex (resp. by x=ex1,y=ex2) when the parameter values varies from a to b, using the formula arcLen(f(x),x,a,b)=
integrate(sqrt(diff(f(x),x)`^`2+1),x,a,b)
or
integrate(sqrt(diff(x(t),t)`^`2+diff(y(t),t)`^`2),t,a,b).
Examples

- Compute the length of the parabola y=x2 from x=0 to x=1.
  Input :
  arcLen(x`^`2,x,0,1)
  or
  arcLen([t,t`^`2],t,0,1)
  Output :
  -1/4*log(sqrt(5)-2)-(-(sqrt(5)))/2
- Compute the length of the curve y=cosh(x) from x=0 to x=ln(2).
  Input :
  arcLen(cosh(x),x,0,log(2))
  Output :
  3/4
- Compute the length of the circle x=cos(t),y=sin(t) from t=0 to t=2*π.
  Input :
  arcLen([cos(t),sin(t)],t,0,2*pi)
  Output :
  2*pi