I'm currently taking multivariable/vector calculus and I'm struggling. It's been well over a year since I took calculus 2, and way longer than that since calculus 1 so I'm trying to play catch-up on old material while learning the new stuff.
I'd really appreciate feedback about my solution to a question asking me to convert a Cartesian coordinate triple integral into an integral in cylindrical coordinates.
Apart from feedback/confirmation, my main concern relates to the integration limits of theta. I'm having a hard time understanding the text on this, and relevant material I've found tends to skimp on the details. I am going to graph the integration limits to get a better idea of what's going on in this problem, but I frequently run out of time during exams and feel that I need to be confident in setting these up through algebra alone.
The problem and attempted solution can be found in the link below. I'm new to the site and it won't allow me to imbed the image in the post.
https://i.stack.imgur.com/quLFl.jpg
For anyone who gave this a read, thank you for taking the time, I really do appreciate it.