00:01
So if we want to find the arc length of this curve from negative 5 to 5, what we're going to need to do is apply the following integral.
00:11
So we're going to integrate from, so a to b of, so it would be dx by dt squared, plus d .y by dt squared, plus dz by dt squared, and then we have the square root of all of that and then we have d t on the outside if we go ahead and find these and then plug everything in from there we should be able to find our arc length so let's go ahead and do that so if we take the derivative and actually let me scoot down a little bit so this is supposed to be x so x is t so if we take the derivative of this with respect to t.
01:01
That will just give us one.
01:05
Then this here is going to be y.
01:07
So we have y is equal to 3 cosine t.
01:10
So we have dy by dt is equal to, well, the derivative of cosine is negative sign.
01:15
So this would be negative 3, sine t.
01:19
And then this is going to be z.
01:23
So z is equal to 3, sine t.
01:26
And then dz by dt, while the derivative of sine is cosine is cosine.
01:31
Be 3 cosine t.
01:34
And now we just need to come down here and plug these in...