Advanced Knowledge Problem of the Week

I hope everyone's enjoying your beautiful or non-beautiful summer, wherever you may be! Here's an Advanced Knowledge Problem of the Week to either give you something to think about in the sun, or give you an excuse to stay out of the rain. 

Like always, you can check out my solution to the problem below.





Did you like this problem? Did you find another way to set up the integral? Let us know in the comments!