Finding Area In Polar Coordinates
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- Опубліковано 28 вер 2024
- 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:
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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 UA-cam TV with the Organic Chemistry Tutor.
This makes much more sense one you realize you're doing a double integral.
this guy is actually a psychic, literally uses most of my hw problems
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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.
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.
He explains it better at 14:15. Just use 3theta instead of theta
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The 3D version of this is spherical harmonics which have a lot to do with orbitals
Thanks dude!!! Super helpful! I have a test on this on Monday and my teacher was soo confusing.
Thank you very much
thank you
Thank you, btw how do we know when to integrate half instead of a full revolution?
thanks! saving me once again!
0:54 that’s a perfect drawing of the alpha α symbol lol I’m not good at writing the alpha symbol correctly
man i love you so much
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?
I tried checking out the video on graphing polar curves and its not available anymore
Can you please re-upload it
Thank you so much!!
Looking for integral proofs that can be used for chemical sensors over time.
شكراً جزيلاً
May I request finding volume in polar coordinates? I’m in calc 3 and I’m lost
how did you know the graph look like that?
refer to his 1 hour video on graphing polar equations, limacons ,cardiods,rose curves,lemniscates,circles,functions & graphs.
Thank you soo much
how to do you find the limits of integration for r=2cos(3thetha)
how do I plot polar coordinates not originating at the origin (0,0)?
U are a lovely man... a godsend
but what if it's r = 3-8cos(x)?
is this there for calc bc?
Have a comment! Algorithm be praised! \o/
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This shit hard
The area enclosed by one petal.... and he says nothing about how to find a petal.
That’s from a previous lesson silly
3 over 2 is half of 3
Me : am i a joke to you ?
???????
Why not just let the funktion equal to 0 when u want the angles😂
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Oi
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)
I mind, thanks for posting!
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I already know about those things lol
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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!
clutch before the test this helped a lot. Easy to make a mistake with signs the other way
Thanks man. This Coronavirus has messed a lot of things up and that includes my calc II class. Thank god we have videos like yours, because it really has helped me doing my class online.
In calc 2 as well. Forced to be online class.
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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.
I always just set r=0 and solve solve for theta to see where the graph hits the pole
What happens if it doesn't hit the origin?
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pause
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
THANKS SO MUCH! I understood in this video all that I couldn't understand in two semesters of engineering!
They teach this stuff to us in sixth form lmao.
@@strangerdanger7616 who cares
never mind i saw where the 2 went
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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Please can you confirm your answer for the last example. In stead of 41Pi/4, I get 41 Pi/2
I got the same
@@indy7155 i think he finished his exam 7 months ago
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We are studying it in Cal I
I don’t get how to find the bounds
I would have drown a cinnamon roll and failed.
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
Why you choose 90 decided to the angel at the second exampel why we don't choose zero or 360?!😢
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I am confused of taking the angles
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I thought it was “lem-niskit”
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what does he say at 1:42? Power rasing or power reducing formulas? ;-;
Because there’s a sin^2(theta) which you can use the power reduction formula of trigonometry. To get rid of the power. It’s a trig identify.
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I hate these lol. They sometimes have u-substitution twice, and when that happens, I always make a mistake :(
hello ,I cant find the video on graphing polar equations ,it shows that the video is unavailable.
thank you so much!! These videos are so helpful and easy to understand.
the video for Graphing Polar Equations is not available anymore ! but thanks for the Video
😍
Seems as thought the link to Graphing Polar Equations video no longer works could please you reupload it?
thanks bro!
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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)
God bless you.
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19:00 Is it just me, or do you guys also think of beltways whenever he says, "inner loop"
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
missing explanation about finding the limits of alpha and beta
Sir if we take (-π/6) and (π/6) limit in question 3. r=1+2sintheta.is this possible.
Never thought of an amazing and easier way to solve it!
Can I not just integrate between o and pi and then divide by two for the second example?
Why not just let the funktion equal to 0 when u want the angles😂
If I want the whole area cannot I just integrate between 0 and 2pi?