Question

Find the arc length for x(t) = t2
and y(t) = 6t3 − 2 where −1 ≤ t ≤ 1.

Answer 1

i'm getting the arc length to be zero, but i know that's not right :/

Answer 2

i'm getting dx/dt to be 2t
dy/dt to be 18t^2

Answer 3

arc length = \[\int\limits_{-1}^{1} \sqrt{4t^2 +324t^4}\]

Answer 4

= \[\int\limits_{-1}^{1} 2t \sqrt{1+81t^2}\]

Answer 5

1+81t^2=u

Answer 6

Du=162t

Answer 7

\[\frac{ 2(1+81t^2)^{3/2} }{ 243 }\]

Answer 8

this is what i got when i integrated it without evaluating at -1 and 1

Answer 9

I hope so

Answer 10

so is it right?