Calculus II: Integration over parametric curves

In this video, we discuss how to compute the region bounded by parametric equations along with a few examples on how to do so.

00:00 - Introduction
00:23 - Area bounded by parametric equations in different situations
04:08 - Example 1
08:23 - Example 2

[MathforThought]

At 3:54, when I wrote the integrals on the right, the bounds should be from c to d and not from a to b although I think it was fairly obvious that was the case.

[iqdjdyu]

how do we identify if we are going in the positive or negative direction ? eg in example 1

[alonzoozar]

For Ex.2, how do you know which integration formula to use for the asteroid?

[nicolasazzolini]

For example 1: Would a and b be the radius measured in the x and y axis respectively (horizontal and vertical)?