Скачать или смотреть Solids of Revolution Examples | Rotating a Region About the Line x = a

📚 Solids of Revolution Example | Rotating a Region About the Line x = a
In this video, we’ll find the volume of a solid of revolution by rotating a region around a vertical line of the form x = a. You’ll see how to identify inner and outer radii, express the radii in terms of y, and use the washer method to evaluate the definite integral. Each example is worked out step by step to help you understand exactly how to set up and solve these problems.

🔍 What You’ll Learn in This Video:
✅ How to identify the region bounded by the curves
✔ How to determine inner and outer radii when rotating about a vertical line
✔ When to integrate with respect to y instead of x
✔ How to apply the washer method:
  V = π ∫ (r_out² – r_in²) dy
✔ How to set up and evaluate the definite integral to find volume
✔ How to interpret the geometry of the region from the graph

📥 Download Free Guided Notes
👉 https://www.understandthemath.com/cal...

Limits and Derivatives
   • The Tangent Problem and the Velocity Probl...  
   • The Limit of a Function| Intuitive, Genera...  
   • How to Calculate Limits Using Limit Laws |...  
   • Precise Definition of a Limit (Epsilon–Del...  
   • Understanding Continuity in Calculus: Defi...  
   • Limits at Infinity and Horizontal Asymptot...  
   • Derivatives and Rates of Change in Calculu...  
   • The Derivative as a Function: Graphing, Di...  
   • The Derivative as a Function: Graphing, Di...  
Differentiation Rules
   • Derivatives of Polynomials and Exponential...  
   • Product Rule and Quotient Rule in Calculus...  
   • Derivatives of Trigonometric Functions: Si...  
   • The Chain Rule in Calculus: How to Differe...  
   • Implicit Differentiation in Calculus: Step...  
   • Derivatives of Inverse Trigonometric Funct...  
   • Derivatives of Logarithmic Functions and L...  
   • Rates of Change in Calculus | Physics, Che...  
   • Exponential Growth and Decay | Population,...  
   • Related Rates in Calculus | 8 Classic Exam...  
   • Linear Approximation and Differentials in ...  
   • Hyperbolic Functions in Calculus | Definit...  
Applications of Differentiation
   • Maximum and Minimum Values in Calculus | C...  
   • The Mean Value Theorem in Calculus | Expla...  
   • How Derivatives Affect the Shape of a Grap...  
   • L’Hôpital’s Rule in Calculus | Indetermina...  
   • Curve Sketching in Calculus | Step-by-Step...  
   • Graphing with Calculus and Technology | Us...  
   • Optimization Problems in Calculus | Step-b...  
   • Newton’s Method Explained | Approximating ...  
   • Antiderivatives | Definition, Formulas, an...  
Integrals
   • The Area Problem | Approximating and Findi...  
   • The Definite Integral | Riemann Sums, Prop...  
   • The Fundamental Theorem of Calculus | Conn...  
   • Indefinite Integrals and the Net Change Th...  
   • The Substitution Rule (U-Substitution) | S...  
Applications of Integration
   • Areas Between Curves | Finding Area with V...  
   • Volumes of Revolution Using Disks and Wash...  
   • Work | Using Integrals to Calculate Work D...  

Visit the Understand The Math Website
https://www.understandthemath.com
Find free guided notes, filled in guided notes for purchase, course playlists, and math merchandise.

Connect & Support
TikTok:   / understandthemath  
Instagram:   / understandthemath  
Facebook: https://www.facebook.com/profile.php?...
Support: https://buymeacoffee.com/understandth...

More About Understand The Math
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.

#Calculus #Calculus1 #SolidsofRevolution #WasherMethod #DiskMethod #VolumeByRotation #ApplicationsOfIntegration #UnderstandTheMath #GuidedNotes #MathVideo