Finding Area of a Circle using Calculus_Part II: Using Polar Coordinates

We use Calculus once again to develop the equation for the area of a circle, however, in this second of our two-part video series, we present a solution using Polar coordinates -- a system far more robust when dealing with circular shapes. We especially note the great economy of computational time and effort afforded us over the solution demonstrated in Part I which considered the analysis in Cartesian (i.e. Rectangular) coordinates

Finding Volume of a Sphere using Triple Integrals in Spherical Coordinates
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Finding Volume of a Sphere using Triple Integrals in Spherical Coordinates

Finding Area of a Circle using Calculus_Part I: Using Rectangular (i.e. Cartesian) Coordinates
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Finding Area of a Circle using Calculus_Part I: Using Rectangular (i.e. Cartesian) Coordinates

Find the Volume of Any Shape Using Calculus
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Find the Volume of Any Shape Using Calculus

Rectangular, cylindrical, and spherical coordinates (introduction & conversion)
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Rectangular, cylindrical, and spherical coordinates (introduction & conversion)

Find the Area of a segment of a circle using Polar Coordinates and  Double Integrals
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Find the Area of a segment of a circle using Polar Coordinates and Double Integrals

The Professor Who Taught People How To Think (1962)
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The Professor Who Taught People How To Think (1962)

263 DIOS TE DICE HOY: ESA ANGUSTIA QUE TE ROBA LA PAZ SERÁ CAMBIADA POR DESCANSO
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263 DIOS TE DICE HOY: ESA ANGUSTIA QUE TE ROBA LA PAZ SERÁ CAMBIADA POR DESCANSO

Integration in Spherical Coordinates
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Integration in Spherical Coordinates

Buying Goats From Farmers | 3-Wheeled Truck Packed Full for Village Market
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Buying Goats From Farmers | 3-Wheeled Truck Packed Full for Village Market

Finding Area In Polar Coordinates
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Finding Area In Polar Coordinates

Unbelievable Smart Worker & Hilarious Fails | Construction Compilation #8 #adamrose #smartworkers
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Unbelievable Smart Worker & Hilarious Fails | Construction Compilation #8 #adamrose #smartworkers

Area Under Polar Curves | Calculus 2 Lesson 49 - JK Math
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Area Under Polar Curves | Calculus 2 Lesson 49 - JK Math

Belgien – Senegal Highlights | Sechzehntelfinale, FIFA WM 2026 | sportstudio
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Belgien – Senegal Highlights | Sechzehntelfinale, FIFA WM 2026 | sportstudio

Deriving Surface Area of a Sphere Using Integration
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Deriving Surface Area of a Sphere Using Integration

ASMR Best Triggers For Sleep Collection (No Talking) 3 Hours of Tapping & Scratching
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ASMR Best Triggers For Sleep Collection (No Talking) 3 Hours of Tapping & Scratching

England vs. DR Congo Highlights FIFA World Cup 2026 | Sportschau
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England vs. DR Congo Highlights FIFA World Cup 2026 | Sportschau

Unbelievable Smart Worker & Hilarious Fails | Construction Compilation #1 #adamrose #smartworkers
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Unbelievable Smart Worker & Hilarious Fails | Construction Compilation #1 #adamrose #smartworkers

Oxford Calculus: Jacobians Explained
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Oxford Calculus: Jacobians Explained

Area Elements (dA) in Polar Coordinates: Introduction to Integrals and Double Integrals
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Area Elements (dA) in Polar Coordinates: Introduction to Integrals and Double Integrals

The Most Misunderstood Concept in Physics
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The Most Misunderstood Concept in Physics