What is the length of the plane curve defined by r(t) = <t^2 + 1, t^3 - 2> for t is an element of [0,2]?

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- Feb 12th 2008, 01:05 PMchaddyFinding Length
What is the length of the plane curve defined by r(t) = <t^2 + 1, t^3 - 2> for t is an element of [0,2]?

- Feb 12th 2008, 01:18 PMgalactus
Arc length for a parametric curve is given by:

- Feb 12th 2008, 02:10 PMchaddy
So would it be

and

So

Is this the right answer? - Feb 12th 2008, 02:30 PMgalactus
Not quite. Aren't your limits of integration 0 to 2?. Use those, not a and b. That was just for an illustration of the formula.

- Feb 12th 2008, 02:53 PMchaddy
Yes, so it would be

Correct? - Feb 12th 2008, 03:01 PMgalactus
Yep. (Clapping)