Surface Area of Revolution of Parametric Equations: X-axis & Y-axis

This calculus 2 video tutorial explains how to find the surface area of revolution of parametric curves about the x-axis and about the y-axis. It contains 2 example problems with the solutions.
Parametric Equations - Introduction: • Parametric Equations I...
Derivatives of Parametric Functions:
• Derivatives of Paramet...
Tangent Lines of Parametric Curves:
• Tangent Lines of Param...
2nd Derivative - Parametric Equations:
• Second Derivatives of ...
3rd Derivative of Parametric Curves:
• Differentiation of Par...
___________________________________
Horizontal & Vertical Tangent Lines:
• Horizontal Tangent Lin...
Area of Parametric Curves:
• Area of Parametric Curves
Arc Length of Parametric Curves:
• Arc Length of Parametr...
Surface Area of Parametric Curves:
• Surface Area of Revolu...
Polar Coordinates - Introduction:
• Polar Coordinates Basi...
Tangent Line Equations - Polar Form:
• Tangent Line Equations...
____________________________________
Horizontal & Vertical Tangents - Polar:
• Horizontal Tangent Lin...
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...
_______________________________________
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[@TheOrganicChemistryTutor]

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an exceptional video/lecture on The Surface Area of Revolution of Parametric Equations about the Xand Y axis. In some Calculus textbooks, Surface Area of Revolution problems are computed in different ways. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@geroavendano7427]

thank you so much, grettings from Guatemala.

[@samiirahmed534]

Thank you sir ....salute from somalia 🇸🇴🇸🇴🇸🇴🇸🇴

[@moucharibe1]

be careful when you working with a interval with a negative number in it when you remove the sqrt of t^2 make sure you put absolute value and then you have to work with two interval when is negative you will put negative sign before and when is positive example [-1,1] after removing sqrt of t^2 that`s will equal to interval [-1,0] -t + [0,1] t . this is very important when you dealing with a change sign in interval

[@fat_table]

this guy is amazing i love him so much

[@user-uh8wk5uy9n]

Find surface area by rotate y=erf(x) about x axis x from -1 to 1

[@globalmalfunction]

Why did you place the Y outside of the integral? It is a variable, not a constant. You cannot take out "y" if it has variables

[@brennanbeell4008]

Certain books represent it that way. The importance of this method is to realize what y is representing. He knew it represented the integrating variable which is why he brought y into the integrand. Well, technically, he didn't bring y into the integrand, he brought t^2. As long as you know wwhat your integrating with respect to, than it's okay

[@shuvanhaldar8320]

it's more to show you that when you are taking the SA of something being revolved around an axis, it is really because you are taking the length(the function) and multiplying it by the circumference of a circle to get the SA. I think I could have worded that better but I think u know what I mean.

[@bobprior6661]

Right. "y" should never have been outside of the integral to begin with. He makes a "correction" by bringing it into the integral eventually, but that is an "illegal" move. The only time a variable can be multiplied into an integral-or factored out of an integral-is when the variable is unrelated to the differential. In this case, y is very related to the differential, dt, and should have been in the integral from the beginning.

[@alejrandom6592]

@@brennanbeell4008 no, it's not okay to use ambigous nonstandard notation. There is no reason why the y should be outside.

[@user-uh8wk5uy9n]

Find the surface area due to the rotation of the area between f(x)=x^3 and g(x)=x

[@zhenglongli385]

why after the t move into the integral, t does not change?

[@rontoolsie]

The t should never have been outside the integral sign to start with. The incremental surface area dA= 2pi.y.dl,where dl is the sqrt of [ (dx/dt)^2 +(dy/dt)^2]. The entire expression then needs to be integrated with the only constant being 2pi since y,dx/dt and dy/dt are all functions of t. This reduces to A=2pi.integral [y(t).sqrt{(dx/dt)^2 +(dy/dt)^2}dt]

[@holyshit922]

x=acos(theta) y=bsin(theta) a=6378 b=6357 Surface area of revolution of this curve is more practical

[@zanejones4122]

why did you not unsub your U's before you evaluated?

[@justinjohn1308]

Hi, a quostion. Why when you divede t^3 by 18t you only remain with t^2 and not t^2/18?

[@atnagnugs3203]

he forgot it. And it did it at 10:55

[@tolgadegirmenci1871]

What happened to 18 at 9:35 ?

[@jam34786]

he includes it back in @ 10:43

[@tolgadegirmenci1871]

@@jam34786 Thank you.

[@Paulog2003]

Jeeeesus huge ass process

[@watertantrums2000]

Sy is confusing ahhh.

[@user-cl5qe7mk6s]

You lost me there at 2: 38 I mean isn't the t outside the integrals to be excluded from intergrating😏

[@moucharibe1]

plz redo this examples you not allow to take the r(x) out of the integration you are changing the definition of the Area of surface of revolution . it work for you this time because you have to cancel the t but all the time , please change otherwise people will make their exams wrong thank you!

[@anthonyajao2156]

That’s how the formula is depending on the axis of rotation check your textbooks

[@alejrandom6592]

2:24 this is very very wrong and misleading, you can't just put functions in and out of an integral like they are constants. That should have not been outside the integral in the first place. The real formulas have the x(t) and the y(t) INSIDE the integrals. Please take down this video.

[@sonyduck8663]

getting the wrong answer

[@yurenchu]

Disliked, because you started with writing y outside the integral, which is mathematically unsound.

[@slips5815]

Your a potato

[@letsplaysomegames985]

Ok yuri renner

[@mikealgraham5549]

yo mama is mathematically unsound

[@piyushshah4265]

@@mikealgraham5549 yo wth🤣🤣

[@suckmyhugewiener633]

don’t hate on my brotha organic chemistry tutor

[@rmdir]

I don't ever want to see you pull a variable out like this again. You have done a lot of good work, but some stuff is unforgivable. You were treading dangerous water here.

[@moucharibe1]

be careful when you working with a interval with a negative number in it when you remove the sqrt of t^2 make sure you put absolute value and then you have to work with two interval when is negative you will put negative sign before and when is positive example [-1,1] after removing sqrt of t^2 that`s will equal to interval [-1,0] -t + [0,1] t . this is very important when you dealing with a change sign in interval