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*$\pi$.
  Input :
  arcLen([cos(t),sin(t)],t,0,2*pi)
  Output :
  2*pi