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2. [-/15 Points] DETAILS OSCALC1 16.8.390-392.WA.TUT.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Use the divergence theorem to evaluate the flux If F. ds. F = (5x3, 0, 523), s is the octant of the sphere x2 + y2 + z2 = 4, in the first octant x 2 0, y 2 0,2 2 0 = Х + + =

Step 1 of 4 Recall how to find the divergence of a vector field F = (F1, F2, F3). div(F) = af1 + 0F2 + ағз ax ay az Recall the divergence theorem. Let : be a closed surface that encloses a region w in R3. Assume that is piecewise smooth and is oriented by normal vectors pointing to the outside of w. Let F be a vector field whose domain contains w. Then we have the following equation. SI F.dS = -SSL . div(F) DV To evaluate the flux, we will need to find the divergence of the vector field F and then use the appropriate coordinates and bounds of integration to integrate the divergence. Calculate div(F) for F = (5x3,0, 523). div(F) = Substitute the ression for div(F) into the equation from the divergence theorem. SIF F. ds = -SIL (O)ov Submit Skip (you cannot come back)