Multivariable Calculus | Two surface integrals over vector fields.

[@giovannimariotte4993]

Incredible explanation but there is a calculus mistake in the dot product of the second integral

[@FelipeHenrique-yq3bu]

About the second surface integral, I got 12 pi as answer, dunno if it's correct, but in the video there's some mistakes in the dot product

[@danielsmith6517]

Just a heads up, 3 of your videos on Surface Integrals aren't in your multivariable calculus playlist!! I was quite confused when the playlist jumped from surface areas to Stoke's theorem. Fantastic videos though, they're incredibly helpful.

[@latifmuhammad8874]

For your last example, the normal is actually pointing in the wrong direction since you have positive 1 as your z component

[@latifmuhammad8874]

z component should be negative if the normal via the cross product is to point outward

[@latifmuhammad8874]

I've got -8π via the divergence thm

[@pedroinacio_maths]

the answer should be -12pi. Did you remember to subtract the surface integral of the top circle in the plane z=4? The divergence theorem gives you the flux across all of the boundaries of the volume