Part C, please. (c) Find the flux of F through S. Show your work, and circle your final answer.(Note: This exercise refers back to the vector field F and the figure on the previous page.) 5. Let F = -9zi+ (xe"² – 2xe²)} + 12 K. Find f, F.dĀ, and let S be the portionof the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (seefigure to the right), oriented upward.y(a) Explain why the formula F ·Ã cannot be used to find the flux of F through the surface S. Please bespecific and use a complete sentence.(b) Can Stokes' Theorem be used to find the flux of F through S? Clearly answer yes or no, and then brieflyexplain your answer.

Name: Part C, please. (c) Find the flux of F through S. Show your work, and
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Part C, please. (c) Find the flux of F through S. Show your work, and circle your final answer.(Note: This exercise refers back to the vector field F and the figure on the previous page.) 5. Let F = -9zi+ (xe"² – 2xe²)} + 12 K. Find f, F.dĀ, and let

c) Given the field equation, F=-9zi+xexz-2xex2j+12k The surface S is the portion of the plane 2x+3z=6 that lies in the first octant such that 0≤y≤4 oriented upwards. Let f(x,y)=z=6-2x3 Then, ndS=-fx,-fy,1dx dy=2, 0, 1dx dyHence, Flux=∬SF·ndS=∬S-9z,xexz-2xex2,12·2, 0, 1 dxdy=∬S-96-2x3,xex6-2x3-2xex2,12·2, 0, 1 dxdy=∫04∫03-36+12x+12dx dy=∫04∫0312x-24dxdy Evaluating the integral, Flux=∫04∫0312x-24dxdy=-72 units