In Thomas's calculus $10^{th}$ edition, chapter $5$, exercises $5.3$, problem $9$, I am asked to find the length of an arc with the equation:
$x=\int^y_0\sqrt{\sec^4(t)-1} dt$
and $\displaystyle {\frac{-\pi}{4}} \leq y \leq {\frac{\pi}{4}}$.
The problem is, I'm not entirely sure what the equation is supposed to be... The previous problems were relatively straight forward, with simple $x=f(y)$ equations. The second part, the parameters of $y$, is confusing me-- is this a parametric of some sort (considering the "$t$")? I've looked around the chapter and can't seem to find another example like it...
If someone could point me in the right direction, that'd be really helpful.