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### Course: Multivariable calculus>Unit 5

Lesson 7: 3D divergence theorem

# Divergence theorem example 1

Example of calculating the flux across a surface by using the Divergence Theorem. Created by Sal Khan.

## Want to join the conversation?

• At isn't the height (z) of the region not always z=1-x^2 ? sometimes it is z=1-x^2 and sometimes it is the plane y=2-z?
• Look at the xz plane, then you should notice that the region of xz plane (which is a region limited by -1<x<1 and 0<z<1-x^2) goes up in the y axis direction limited by y=2-z .

I hope this solves your answer because i don't know to write english properly, :P

Saludos-
• At the beginning of the video, shouldn't the surface integral also be dotted with the normal vector of the surface in order to get the flux?
• Because the function (a*x^2 + b*x^4 + c*x^6) is even, shouldn't we multiply it by 2 and change the limit of integration of x to be from 0 to 1? That way we would get a different result from zero... 5/3.
• (a*x^2 + b*x^4 + c*x^6) is not the function that is integrated. It is a function of the form (a*x + b*x^3 + c*x^5) which is odd. Only after the integration we get the even function.
• For triple integrals, how do you know which variable to integrate with respect to first?
• Most of the time, it won't matter, just make sure the last one doesn't end up with variables
• isn't d(xy)/dx=y ? so shouldn't div F be x+y?
(1 vote)
• Remember that when you are taking the divergence you are taking the partial of each term with respect to that term's "direction". So you are taking the partial with respect to y of the second term. That gives:
d(xy)/dy = x
• How do I decide if I should use green’s, stoke’s, or divergence?
• Does that triple integral in the divergence theorem count as a volume integral?
(1 vote)
• yes. but you are suppose to insert some function inside the integral which is the result of the divergence of F.