00:02
All right, so what we want to do is evaluate the length of the curve, as described by vector function r of t, which we can write in terms of its three component functions, t, three cosine of t, and three sign of t.
00:23
And that's defined on the interval from negative five to five.
00:30
So to do this, we want to be able to use our formula for the length of a curve as described by r of t.
00:40
So this is l is equal to the integral from a to b of the magnitude of the derivative of the vector function with respect to t.
00:55
So the first thing we want to do is take the derivative of our vector function.
01:02
So we have r prime of t.
01:08
And the way we do this is just taking, by taking the derivative with respect to t of each of our component functions.
01:14
So we'll have one for the first, negative 3 sine of t for the second, and 3 cosine of t for the third...