The double integral over a region can be expressed in two different ways. It could be that we write dxdy which means that we integrate with respect to x first and then y (called horizontal strip). Or it could be dydx which means y is integrated first and then x (vertical strips). The big idea is we can convert between these and so can choose whichever is the easier of the two. The steps are:
1) Given an integral, sketch the region implied by the limits of integration
2) Now interpret that region the opposite way, such as vertical strips instead of horizontal strips
3) Write the new integral in the opposite order of integration
4) Hopefully it will now be easier to compute!

****************************************************
COURSE PLAYLISTS:

►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...  

► CALCULUS II:    • Calculus II (Integration Methods, Ser...  

►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...  

►DIFFERENTIAL EQUATIONS (Calc IV):    • How to solve ODEs with infinite serie...  

►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...  

►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  

***************************************************

► Want to learn math effectively? Check out my "Learning Math" Series:
   • 5 Tips To Make Math Practice Problems...  


►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