Скачать с ютуб Calculus 3, Cartesian Triple Integral Convert to Spherical Coordinates | Multivariable Calculus в хорошем качестве

Calculus 3, Cartesian Triple Integral Convert to Spherical Coordinates | Multivariable Calculus

We convert a Cartesian coordinate system triple integral into spherical coordinates to define by a hemisphere above the yz-plane. We begin by analyzing the given bounds in Cartesian coordinates and deducing that the region forms a hemisphere. The process includes sketching the region and transforming the coordinates. We demonstrate how to set the proper limits of integration and use spherical coordinates effectively, focusing on the radius (ρ), azimuthal angle (θ), and declination angle (φ). This conversion drastically simplifies the integral, making it much easier. So, in this video we delve into this multivariable calculus here at High Peak Education. ------------------------------------ Chapters / Timestamps 00:00 Introduction 00:38 Why Convert to Spherical 01:18 Understand Cartesian bounds 02:31 xz Plane Semicircle sketch 03:33 y bounds, Sphere of radius 5 05:00 3-Dimensional sketch 07:09 Hemisphere above yz Plane discovered 08:29 Spherical coordinates bounds 13:18 Octants 13:51 Substitute spherical coordinates 14:17 Seperate Triple Integral to Multiply 15:22 Summary 16:34 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