Consider the curve $$y = x + \sin(x),\quad 0 \le x \le 2 \pi .$$ (a) Divide $[0, 2 \pi ]$ up into 1,2, and 4 equal segments, and draw line segments between those values on the graph. Then compute the length of the polygonal curve you drew.

Length for $n = 1$:

Length for $n = 2$:

Length for $n = 4$:

(b) Use a calculator or a computer algebra system to find the length of the curve to four decimal places.

Length of curve $\approx$