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:

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

$L = 28.7405$

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