¿Cómo se calcula el Área de una Dona (Toro)? Usando INTEGRALES

In this video, we'll see how to calculate the surface area of ​​a torus, which is generated by rotating a circle centered outside the origin. We'll do this using an integral that depends on the arc length. We'll also see an interesting result that relates the area and volume of the torus to the length and area of ​​the generating circle (Pappus-Guldin Theorem). ⏮️ Previous:    • ¡El Sorprendente Cuerno de Gabriel! Superf...   ⏭️ Next (Pappus): ▶️ Surface Area:    • Área de Superficies (Usando integrales)   ▶️ Length of Curves:    • Longitud de Curvas (Usando integrales)   ▶️ Volumes of Revolution:    • Volumen de revolución (Sólidos de revoluci...   ❇️ ANSWERS:    • 💎 Área de Esferoide Oblato y Prolato (Supe...   Exercise 8.2.38 from James Stewart's Calculus textbook 00:00 Introduction to calculating the area of ​​a torus 00:15 Generating curve and rotation about the Y-axis 00:35 Equation of the circle (Analytic Geometry) 02:11 Formula for the surface of revolution (Y-axis) 03:52 Solving for the variable y and symmetry 05:37 Integration interval for the X-axis 06:15 Calculating the derivative of the function 07:13 Substitution in the surface formula 07:59 Simplifying the algebraic expression 09:42 Integration method: Change of variable (u) 11:58 Separation into two integrals and solution 13:51 Application of the arcsine and limits of integration 15:20 Final formula for the surface area of ​​the torus 16:15 Relationship with the Theorem of Pappus-Guldin 18:27 Suggested Exercises: Ellipsoids and Memberships #calculus #easymath #math 🚥🚥🚥🚥🚥🚥🚥🚥🚥 🎞️ CHECK OUT MORE FREE COURSES 🎞️ 📖 Math Review Course (Pre-University)    • Curso de Repaso de Matemáticas   🔢 Fractions:    • Fracciones DESDE CERO (Todo sobre FRACCIONES)   ✏️ Arithmetic:    • Curso Completo de Aritmética   🧮 Elementary Algebra:    • Curso Completo de Álgebra   📐 Elementary Geometry:    • Curso Completo de Geometría Elemental   🌟 Trigonometry:    • Curso Completo de Trigonometría   💫 Analytic Geometry:    • Curso completo de Geometría Analítica   📈 Functions:    • Funciones   🌀 Limits:    • Límites   ❄️ Derivatives:    • Curso Completo de Derivadas   🎢 Applications of Derivatives:    • Aplicaciones de las DERIVADAS   🔥 Integrals:    • Curso Completo de Integrales - Cálculo Int...   🎡 Applications of Integrals:    • Aplicaciones de las Integrales   ☕ Ordinary Differential Equations (ODEs):    • Curso Completo de Ecuaciones Diferenciales   🌉 Partial Differential Equations (PDEs):    • Curso Completo de Ecuaciones en derivadas ...   🔬 Applications of Differential Equations:    • Aplicaciones de Ecuaciones Diferenciales   ➿ Linear Algebra:    • Curso de ÁLGEBRA LINEAL   🎈 Multivariable Calculus (Vector Calculus):    • Curso Completo de Cálculo de varias variab...   💎 Exclusive Videos 💎:    • Members-only videos   🚥🚥🚥🚥🚥🚥🚥🚥🚥 🪐 ALL MY COURSES 🪐 🔗 https://matefacil.net/ 🚥🚥🚥🚥🚥🚥🚥🚥🚥 📚 BIBLIOGRAPHY 📖 📙 Calculus of One Variable, James Stewart 📗 Calculus, M. Spivak 📘 Calculus, Tom M. Apóstol 📕 Infinitesimal Calculus of One Variable, Juan de Burgos 📙 Calculus, Bartle 📗 Calculus with Analytic Geometry, Swokowski 📘 Calculus, Lang 📕 Calculus, Kuratowski 📙 Calculus, Frank Ayres (Schaum's Outline) 📗 Differential and Integral Calculus, Piskunov (MIR) 🚥🚥🚥🚥🚥🚥🚥🚥🚥 🏦 DONATIONS 🙏 🅿️ Paypal: https://www.paypal.com/cgi-bin/webscr... 💎 Channel Memberships:    / @matefacilyt   🔸 Patreon:   / matefacil   🚥🚥🚥🚥🚥🚥🚥🚥🚥 🛜 MY OTHER CHANNELS AND SOCIAL MEDIA 🛜 🟪 Telegram Group: https://t.me/matefacilgrupo 🟥 Physics Channel:    / @matefacilfisica   🟩 Personal Channel:    / @matefacily   ⬛ Twitch:   / matefacil   🟦 Facebook (Page):   / matefacilyt   🟫 Twitter:   / matefacilx   🟧 Instagram:   / matefacilx   ⬜ TikTok:   / matefacilx   🟨 Discord:   / discord   🚥🚥🚥🚥🚥🚥🚥🚥🚥 #Mathematics #Math #tutorials #teacher __________________________________