I need help figuring out the wording to this Calc 2 problem

Question

anonymous · Answer

Consider the parametric equation $$x = 16(\cos \theta + \theta \sin \theta)$$
$$y = 16( \sin \theta - \theta \cos \theta)$$
What is the length of the curve for $$0 \le \theta \le \frac{ 11 }{ 8 }\pi$$

anonymous · Answer

I understand what the arc length means, but the equations have two separate arcs over the interval

anonymous · Answer

@mathstudent55  you seem like the most qualified person answering right now, I just need to understand what it's asking for, I can do the math myself

amistre64 · Answer

$$\int_{a}^{b} ds$$
given that ds is
$$ds=\sqrt{(x')^2+(y')^2}dt$$

anonymous · Answer

Where does this equation come from? Just so I have a base of understanding. I don't remember seeing anything like that in lecture

amistre64 · Answer

its just the result of takeing the segment of an arc ... and comparing it to a right triangle

amistre64 · Answer

|dw:1439771344418:dw|

amistre64 · Answer

as we work our way to infinitesimals we get:

|dw:1439771398544:dw|

and the pythag takes care of the rest