Determining the Length of a Curve - Page 13

Questions
  • For which function does the integral integral 0^3 sqrt(1+16e^4x)dx give the length of the curve on the interval [0,3] ?
  • What is the arc length of the curve given by #x = t^2-t# and #y= t^2 -1#, for # 1<t<5#?
  • What is the arc length of the curve given by #x =sqrt( t^2+t+1)# and #y= 1/(t^2+1) -t#, for # 0<t<1#?
  • Calculate the length of the curve? #x = cos(t)+sin(t), y=cos(t)-sin(t)#
  • What is the arclength of f(t)=(3t^2-1, 3t^3-t) on t∈[-1/sqrt(3),1/sqrt(3)]?