Surface Area of Revolution of Polar Curves

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This calculus 2 video tutorial explains how to find the surface area of revolution of polar curves. It explains how to find the surface area of by rotating the curve about the polar axis and about the line theta equals pi/2. This video explains how to calculate the surface area of a sphere using calculus and geometry.

Area of Parametric Curves:

Area of Polar Curves:

Area Between Polar Curves:

Arc Length of Polar Curves:

Surface Area of Polar Curves:

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Writing Equations of Ellipses:

Eccentricity of an Ellipse:

Area of an Ellipse:

Circumference of an Ellipse:

Hyperbolas - Conic Sections:

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Parabolas - Conic Sections:

Polar Equations of Conic Sections:

Calculus 3 - Intro to Vectors:

Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

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Professor Organic Chemistry Tutor, thank you for a solid explanation and analysis of the Surface Area of Revolution of Polar Curves in Calculus Two. Reading and doing problems from a variety of Calculus textbooks, I cannot remember seeing this classic material on Surface Area of Revolution of Polar Curves. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

georgesadler

At 4:35 I'm not sure if I miss anything here but aren't the equations in line 2 and 3 wrong? Bacause the right side of the equations are not the value of the surface area.
Also, the right side of the equation in line 3 and 4 are not equal. I don't think you can move r in and out of the integral like that since it is a function of zeta.

coollieeBEAU

At 4:17, how can you move 2 sin (theta) to the right side of the integral?

sharonsolana

What if the revolution occurs at theta=pi or theta=3pi/2, what formula do we use then, or do we tweak the formulas shown here somehow?

Chrisymcmb

What if they didnt give the upper and lower limit? How to determine their limit?

izzaimi

Thank you soo much.
And also you got any social media?

talal

Sin aquare that's plus cos square that's equala to 1

johnbatchler

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