### Chain Rule & Integration by Substitution

Fluency exercise

Parametric equations for nine curves are defined by combining the row and column headings in the table below. The domain of $t$ for each curve is the set of values of $t$ for which the $x$ and $y$ coordinates are defined.
All the functions here were either odd or even, so we were able to use symmetry as a way to look at these curves. For more general parametric equations, we can think about the ranges of $x$- and $y$-values, find coordinates of points for specific values of $t$, and think about how a point on the curve moves as $t$ increases. In some cases, eliminating $t$ and working with a Cartesian equation can be helpful.