Finding Area In Polar Coordinates

This Calculus 2 video tutorial explains how to find the area of a polar curve in polar coordinates. It provides resources on how to graph a polar equation and how to find the area of the shaded region. It contains plenty of examples and practice problems on how to find the area of one loop or of one petal and how to find the area of the inner loop as well.
Area of Parametric Curves: • Area of Parametric Curves
Area of Polar Curves:
• Finding Area In Polar ...
Area Between Polar Curves:
• Finding Area Bounded B...
Arc Length of Polar Curves:
• Arc Length of Polar Cu...
Surface Area of Polar Curves:
• Surface Area of Revolu...
_____________________________
Writing Equations of Ellipses:
• Writing Equations of E...
Eccentricity of an Ellipse:
• Eccentricity of an Ell...
Area of an Ellipse:
• Area of an Ellipse
Circumference of an Ellipse:
• Circumference of an El...
Hyperbolas - Conic Sections:
• Hyperbolas - Conic Sec...
______________________________
Parabolas - Conic Sections:
• Finding The Focus and ...
Polar Equations of Conic Sections:
• Polar Equations of Con...
Calculus 3 - Intro to Vectors:
• Calculus 3 - Intro To ...
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

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Don't mind me. 0:10 rose curve 4:20 rose curve 9:40 Lemniscate 13:32 Circle 18:03 Limacon (inner loop) 30:05 Limacon (no dimple, no inner loop)

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[@caelanhassett8392]

Hey everyone, in case you weren't aware when you have symmetry over either the x-axis or y-axis and the bounds are reciprocals (ex: pi/6 and -pi/6 or pi/2 and -pi/2), you can set the lower limit of integration to 0 (so for ex: -pi/2 to pi/2 becomes 0 to pi/2) and put a two on the outside of the integral (multiplying the whole integral by two). I noticed when following along and doing the problems myself that it made the algebra at the end of the problem simpler (the zero made things easy). Hope this helps!

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[@tizzlerizzle9673]

At 7:00 ish he says it’s intuition, but it can be found by solving for where theta equals 0. This is because the graph passes through the origin and it is bound between pi/2 and 0, so we know that for cos3x to equal 0, it must equal pi/2. Pi/2 divided by 3 = pi/6.

[@bugsfudd8295]

I always just set r=0 and solve solve for theta to see where the graph hits the pole

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What happens if it doesn't hit the origin?

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a fantastic video/lecture on Finding Areas in Polar Coordinates in Calculus Two. Finding the Area of a Polar Curve in Polar Coordinates is not a difficult task; However, the real problem is finding the correct limits of Integration when computing the Area. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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[@prashantbhatta8759]

why we divided 90/2 in first case and and 90/3 in second case? Why by 90? Can you focus on finding angle and made it more clear.

[@methoril]

in the unit circle, 180°(degrees) is equal to π (rad). so π/2 is 90°. He chose 90 or π/2 to be the upper limit because it is where the loop closed.

[@FreeBirdVince]

He explains it better at 14:15. Just use 3theta instead of theta

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[@paulzupan3732]

For the first problem, shouldn't the final answer be multiplied by 4? If we're integrating between 0 and pi/2, isn't that only a quarter of the whole polar curve? EDIT: I'm stupid, the question was to find the area of one petal. Bruh

[@juliejeff6349]

Never thought of an amazing and easier way to solve it!

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[@gracefulgrizzly39]

This makes much more sense one you realize you're doing a double integral.

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[@mattweiman5144]

For the second example, could you just find the area from pi/2 to pi? Wouldn't that be the same thing since all the petals are symmetric?

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[@dani3lalal306]

the video for Graphing Polar Equations is not available anymore ! but thanks for the Video 😍

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[@helenerivard7016]

Please can you confirm your answer for the last example. In stead of 41Pi/4, I get 41 Pi/2

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I got the same

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[@gabrialtome4478]

The 3D version of this is spherical harmonics which have a lot to do with orbitals

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[@racheladamson7610]

I thought for even numbers petals are 2n based on your last video, so how come at 11:15 you draw 2 instead of 4

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This blew my mind

[@goodc.2853]

To find the limits of integration, is graphing the only way in truly knowing what the bounds are? I.e. is there a different method in which you could find the bounds as well?

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Thank you, btw how do we know when to integrate half instead of a full revolution?

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[@AvaFindee]

for the first example, aren't we supposed to multiply the entire thing by 4 if we were to find the area of all four leaves? Looking forward for an answer, got a final very soon.

[@WilliamQuinones]

Hope im not too late but the question said the area of ONE petal. If it were all 4 leaves, then yes you would multiply by 4.

[@iMAANfinity]

how did you know the graph look like that?

[@phillipyt8876]

refer to his 1 hour video on graphing polar equations, limacons ,cardiods,rose curves,lemniscates,circles,functions & graphs.

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شكراً جزيلاً

[@ivanfranco3876]

I don’t get how to find the bounds

[@ws8288]

Thank you soo much

[@NguyễnLong-o1t]

thanks bro!

[@samsonschiff1944]

Seems as thought the link to Graphing Polar Equations video no longer works could please you reupload it?

[@lorrainetelino7621]

Thanks for the help😉

[@Kerry.]

Thank you!!!

[@gregorystocker971]

Why do we use 90deg to calculate our angle? When talking about r = 2cos(3•theta) you get between -pi/6 and pi/6. Is it just because that represents the first quadrant?

[@donny6016]

Thank you!

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God bless you.

[@magdalenadjuulume7217]

I tried checking out the video on graphing polar curves and its not available anymore Can you please re-upload it

[@milindusha]

Can I not just integrate between o and pi and then divide by two for the second example?

[@danarenee2931]

May I request finding volume in polar coordinates? I’m in calc 3 and I’m lost

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[@anupriyan564]

I am confused of taking the angles

[@edgardoconcepcion8308]

y did u subtracted to 2π to 11π/3 to become 5π/3? what's d reason behind it? when s d right time to this? reply plz. thx

[@Justin-hh25]

For the bounds at 14:30, instead of doing -pi/2 to pi/2, could you instead write it as pi/2 to 3pi/2?

[@Justin-hh25]

Same question applies for the very last problem too

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Looking for integral proofs that can be used for chemical sensors over time.

[@Algebrainiac]

0:54 that’s a perfect drawing of the alpha α symbol lol I’m not good at writing the alpha symbol correctly

[@milindusha]

If I want the whole area cannot I just integrate between 0 and 2pi?

[@habibarafique4129]

hello ,I cant find the video on graphing polar equations ,it shows that the video is unavailable.

[@xXGoocaXx]

Thank you soo much :)

[@videogamy6032]

Shouldn't the answer be on the first problem be pi/4? I think you skipped a step on using u-sub before integrating cos(4theta)

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[@vumanimoyo2203]

never mind i saw where the 2 went

[@ghaustariq5594]

how to do you find the limits of integration for r=2cos(3thetha)

[@aamirqureshi4611]

Sir if we take (-π/6) and (π/6) limit in question 3. r=1+2sintheta.is this possible.

[@noorulhuda2426]

Thanks alotttt

[@kishorekumarsathishkumar1562]

Where does that 1/2 r^2 d(theta) come from?