You've reached the end of Multi-variable Calculus! In this video we generalized the good old "u-subs" of first year calculus to multivariable case with a multivariable change of variables. The trick is to set up a new coordinate system where the messy region before is now very nice, perhaps just a rectangle. We have to be careful though as we have to multiply our integrands by a scaling factors called the Jacobian. In this video I sketch the intuition behind the Jacobian and compute it out in an example. **************************************************** 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: ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON: ►MATH BOOKS I LOVE (affiliate link): ►CURIOSITY BOX: use CODE drtrefor for 25% off awesome STEM merch boxes COURSE PLAYLISTS: ►DISCRETE MATH: ►LINEAR ALGEBRA: ►CALCULUS I: ►CALCULUS II: ►MULTIVARIABLE CALCULUS (Calc III): ►VECTOR CALCULUS (Calc IV): ►DIFFERENTIAL EQUATIONS: ►LAPLACE TRANSFORM: ►GAME THEORY: OTHER PLAYLISTS: ►Cool Math Series: ►Learning Math Series: ►LaTeX: SOCIALS: ►X/Twitter: ►TikTok: @drtrefor ►Instagram (photography based):