Double Integration Example over General Regions --- two ways!

We introduced double integration originally for rectangular regions. Rectangular regions were nice because the limits of integration were all numbers. But what about if we want to calculate the volume under a surface over a more general non-rectangular region? In this video we look a full example of a general region and how we can think about breaking the region up into either little vertical strips or little horizontal strips. That is, we compute the double integration either first integrating with respect to x and then y, or switch the order. While this example worked both ways, in some double integral you will want to change the order of integration because only one of the two ways will be easy to actually compute. **************************************************** YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems! **************************************************** ►Full Multivariable Calculus Playlist:    • Calculus III: Multivariable Calculus (Vect...   **************************************************** Other Course Playlists: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series:    • 5 Tips To Make Math Practice Problems Actu...   ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   **************************************************** ►Follow me on Twitter:   / treforbazett   ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett