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Arc Length Formula - -₀∫ⁿ [1 + ƒ'(x)²] Volume of Solid of Revolution (Disk) - -π ₀∫ⁿ ƒ(x)² Volume of Solid of Revolution (Washer) - -π ₀∫ⁿ ƒ(x)² - g(x)² Surface Area of Solid of Revolution - -2π ₀∫ⁿ ƒ(x) √[1 + ƒ'(x)²] * arc length × f(x) × 2π Work Required - -₀∫ⁿ F × D Work Required (Spring/Chain/Rope) - -₀∫ⁿ kx *k = spring constant

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Complete Solutions Manual for A Short Introduction to Mathematical Concepts in Physics, 1st Edition by Jim Napolitano ; ISBN13: 9781032404301. (Full Chapters included Chapter 1 to 9).... 1. Basic Concepts 2. Infinite Series 3. Ordinary Differential Equations 4. Vector Calculus and Partial Differential Equations 5. Fourier Analysis 6. Vectors and Matrices 7. Calculus of Variations 8. Functions of a Complex Variable 9. Probability and Statistics