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We tackle triple integral multivariable calculus problem over a tetrahedron. In this video Paul Quelet of High Peak Education carefully sets up and solve the triple integral by determining bounds and integrating over the given region. Along the way, we provide side explanations on the Divergence Theorem, Stokes' Theorem, and integration by parts to enhance your understanding. This video is perfect for students looking to master the intricacies of multivariable integration and applying calculus concepts over a volume region. ------------------------------------ Chapters / Timestamps 00:00 Vector Fields, Line Integrals, Parameterizations 07:39 Divergence Theorem, Stokes' Theorem 14:13 Triple Integral Setup 19:13 Integration by Parts, When to Use 21:56 Triple Integral Steps to Solve 22:25 Tetrahedron Sketch xyz axes 26:45 Projections onto xy plane, xz plane, yz plane 32:49 Integral Bounds and Setup 36:14 Integration process 40:40 Definate Integral Numerical Final Answer 46:29 Take action! ------------------------------------ Please support us on Patreon: https://www.patreon.com/highpeakeduca... Please follow us on Facebook: / high-peak-education-110762917338673 Please follow us on Twitter: / highpeakeducate Please follow us on Instagram: / highpeakeducation Please follow us on Reddit: / highpeakeducation Please follow us on TikTok: / highpeakeducation Interact with us on Twitch: / highpeakeducation Interact with us on Discord: / discord #HighPeakEducation #MultivariableCalculus #VectorCalculus