Find the lengths of the following curves:

a. \(y(x)=x\) for \(x \in[0,2]\).

b. \((x, y, z)=(t, \ln t, 2 \sqrt{2} t)\) for \(1 \leq t \leq 2\).

c. \(y(x)=\cosh x, x \in[-2,2]\). (Recall the hanging chain example from classical dynamics.)