Recall that a curve can be defined parametrically. For example

Suppose we wanted to find the area under one of the arches of the curve:

One approach could be to eliminate $t$, and find the Cartesian equation of the curve in the form $y=f(x),$ and then integrate as normal. However, this is sometimes inconvenient. As we will see, parametric integration can save us a lot of work.

The curve below is given by the parametric equations

Find the value of the shaded area.