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

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Answer 1 · 2016-10-23T21:27:00

#dx/dt = 3#

#dy/dt = 3t^2 - 2#

Let L = the arclength

#L = int_a^bsqrt((dx/dt)^2 + (dy/dt)^2)dt#

Substituting in our values:

#L = int_-1^2sqrt((9)^2 + (3t^2 - 2)^2)dt#

#L = 28.7405#