Example of a flux integral, Multivariable Calculus

Let's find the flux of F(x,y,z) = (x,z,0) across the paraboloid z=x^2+y^2 with outward-pointing orthogonal vectors. We go through how to set up this vector surface integral computation and then compute it. Error: at 8:10 I pulled -2 out front, but didn't change the sign of the second term (luckily that term has an integral of 0, so the final answer is correct).

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#calculus #multivariablecalculus #mathematics #flux #iitjammathematics #calculus3 #surfaceintegral

[rosskious]

Smart, does the problems, and explains the details, plus you don’t joke around but gets to the problem at hand. What more could you ask for. You should have a LOT more views. Even though you are extremely pretty, you do it with class and does not distract for the presentation.

[GLENNSCHEXNAYDER-nc]

It appears that there was a sign error when factoring out the -2. The second (sin(v)) component should have a positive coefficient, but it ended up not mattering because the whole thing evaluated to zero in the end.

[ussamafadili]

Thank you
You helped us
Thank you from the heart ❤️

[adeeba]

MANY MANY THANKS AND MANY MANY HEARTS AND ROSES TO YOU DR.BELVIN.SINCERELY YOURS
ADEEB.ADEEB.

[retiredaccount]

This is an excellent video. Thank you.

[eswyatt]

Ha! I just wrapped up Units 6 and 7 of this series, with notes coming in at 107 pages. Now I must add.

[moondxstq]

Hi could you explain more the differences between upward/downward normal, inward/outward, and positive/negative orientation?

[amandaliu]

Hi, when I tried to do this question without parameterising the surface (I used dot product of F and the partial derivatives of z) I got -40π instead of 40π. Is it because I used upward pointing normal instead of downward pointing normal? Thank you so much

[sportmaster]

When I use Gauss' Divergence Theorem I obtain a different answer of 64pi, how come?

[glennschexnayder]

I think I’m misunderstanding something. It looks like there’s no intersection of the vector field and the paraboloid, so I don’t understand how it can affect the flux across the surface. The vector field is completely contained in the x, y plane, is it not? What am I missing?