# What is the arc length of #f(t)=(t^2-4t,5-1/t) # over #t in [3,4] #?

##### 1 Answer

Nov 16, 2016

Define

#{ (x(t)=t^2-4t), (y(t)=5-1/t) :} => f(t) = (x(t), y(t)) #

Differentiating

# dx/dt = 2t-4 #

# dy/dt = 1/t^2 #

Then the arc length of

# L = int_alpha^beta sqrt((dx/dt)^2+(dy/dt)^2) #

So over

This definite integral does not have an intrinsic solution and would need to be solved numerically, using either a computer or estimated using the Trapezium Rule or Simpson's Rule