In this video, around the 5:20 mark, YouTuber MindYourDecisions converts the double integral from rectangular coordinates to polar coordinates so as to make the evaluation easier.
However, I fail to see how he managed to get the limits on the radius as $0$ and $\frac{1}{\cos\theta}$. Since the length of the adjacent side is always $1$, shouldn't the limits be $1\leq r \leq \sec\theta$?
The same result is obtained in this article. Thanks for any input. Sorry that I'm not seeing this.
For a vertical line we have the equation
$$ x=1 $$
But in polar coordinates $x=r \cos(\theta)$. Our equation becomes
$$ r \cos(\theta)=1 $$
$$ r = 1 / \cos(\theta)$$
The integration region includes the origin. The radius of the origin is $0$. $r$ is also nonnegative. Therefore the smallest value of $r$ is $0$.