Question

Use the Divergence Theorem to calculate the flux of
F = x^2 i  + (4y − 2xy) j  + 5z k 
through a sphere of radius 3 centered at the origin and oriented outward.

Answer 1

Do you really need help or?

Answer 2

use it ?

Answer 3

so is it just the divergence * the area of the sphere

Answer 4

Yep if the divergece is constant

Answer 5

and it looks like a constant here

Answer 6

you mean divergence * volume of sphere, rgith ?

Answer 7

div F = 2x+(4-2x)+5

Answer 8

yeah the volume my bad

Answer 9

good, because the divergence thm converts area problem into a volume problem

Answer 10

so 2x+(4-2x)+5 * 27(4/3)pi?

Answer 11

i think you can simplify the expression a bit before multiplying

Answer 12

2x and -2x cancel out

Answer 13

yeah

Answer 14

so volume times 9

Answer 15

Yep

Answer 16

you're allowed to do this only because the divergence is constant.
otherwuse, you will have to setup the triple integral

Answer 17

thanks