Surface integral example part 1: Parameterizing the unit sphere | Khan Academy

Visualizing a suitable parameterization

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[cormacavila]

this helped so much, its amazing how math becomes interesting instead of a hassle once I understand the reasoning behind it. thank you

[eldizo_]

This is glorious. I've watched a handful of videos over topics I haven't even covered during my classes and it always leaves me wanting more. Finishing Calc II this semester left me wanting so much more, maybe I'll go be productive during the summer.

[kalanakavishanka]

Best teacher I've ever listened to

[DonRonRaven]

This is just awesome - the guy in the video did an awesome job!

[SDCB]

Thank you Mr. Khan! This makes a lot more sense now

[jkinsella]

I found this conceptually simpler than the example with the torus, so I'd recommend they switch the order in the playlist.

[advaita]

Can I take t from 0 to pi??
Like in polar coordinates

[DonRonRaven]

i think the main confusion in understanding (at least for me) the parametrisation of the sphere is that points on the surface of the sphere don't need to be laying on the unit circle in the x, y plane!

[engr.irshadullahfacultymem]

Similar parametrization to spherical coordinate systems except t measure from xy plan instead from z axis and roh is cost here. But anyhow, this is an interesting perspective of the same problem.

[anthonygarant]

Wouldn't have been simpler to parametrize using polar coordinates?

[yisangwoo]

Why we double integrate x sqrd times d sigma to get the surface of the sphere???

[slimshady]

Hey khan could you make more biology and chemistry videos please

[prshrf]

Just one thing... I didn't quite understand why he picked radius to be 1 (is it because he's talking about unit sphere?). But yea, in spherical coordinates we can express anything in terms of theta, phi and r. or in this case, s, t and r=1.

[x_ma_ryu_x]

when we do the cross product - how do we know which is the right order - rt x rs or the opposite as you will get teh same answer times (-1). and later when you multiply it by FOr example the function to get the flux the answer will be different depending on how you took the order of the cross

[LegaleseLiteracy]

9th comment thanks for your videos i'm a 8 grade honors student at my private school and i love to get ahead and impress even my teachers so thank you :)

[Nikifuj]

Isn't it just 4*pi^2? You didn't have to do all that integration; just revolve the unit circle around the y-axis. The circumference is 2*pi*r^2 = 2, and to get the surface area, you just multiply it by 2*pi again. It's like unfolding it into a rectangle.

[Saptarshi.Sarkar]

Can't I take limit of t from 0 to 2pi?

[TheHarperad]

Man, a unit sphere is the same as a unit circle but 3d instead of 2d, which means it has the radius = 1.

[PartVIII]

you failed because of khan? khan is a useful tool, not a limiting factor.

[ManojKumar-cjoj]

x=r*cost*coss, y=r*cost*sins, z=r*sint🤣🤣🤣