I am trying to figure out the following arc length problem, and it's really coming down to a question over intregration.(adsbygoogle = window.adsbygoogle || []).push({});

Compute the length of the curve r(t)=(4t)i +(4t)j+(t^2+6k) over the interval 0 to 6.

I have dr/dt = (4, 4, 2t) , and then used the arc length equation:

L= integral 0,6 ( sqrt((4^2)+(4^2) +(2t)^2)

and have reduced this to 2 int((sqrt(t^2+8))

I'm doing this to prepare for a test, and have "cheated" by using my calculator to get an answer of 2(6*sqrt(11) + 4*arcsinh(3/sqrt(2))) . I have no idea how to do the intregration of the sqrt(t^2 +8) and would greatly appreciate some advice. Thank you

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# Arc Length intregration

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