00:01
We want to use some kind of cas software to help us calculate the total length to two decimal places of the curve r is equal to theta times sine of theta, which is figure 24, with theta bound between 0 and 4 pi.
00:18
So we will use the equation that we have in the top left of the screen.
00:25
And the only thing we still need to find is what our derivative is.
00:30
So r prime will be, so to take the derivative of this, we'll need to use product rule.
00:36
So the derivative of theta is just 1, so we'd have sine of theta.
00:41
And then we need to take the derivative of sine, and that would be cosine theta.
00:46
So this here should be r prime.
00:49
Now we just plug everything in.
00:52
And so doing that, we would get, so the integral from 0 to 4 pi square root, and then we square our original function, which would give us theta squared, sine squared theta, and then we add, and it looks like i'll actually need to expand the screen a little, then we square our derivative, and we could just leave it like this here, but when you're plugging these things into some kind of software, it's normally a good idea to simplify it down as much as you can because it'll speed up the computation time.
01:39
So let's go ahead and see what we get...
