Divergence Thereom help please? 17.8.19Question HelpUse the Divergence Theorem to compute the net outward flux of the field F = (x,2y, - z) across the surface S, where S is the boundary of the tetrahedron in the firstoctant formed by the plane x +y + z = 1.The net outward flux across the boundary of the tetrahedron is(Type an exact answer, using n as needed.)

Name: Divergence Thereom help please? 17.8.19Question HelpUse the Divergence
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Description: Divergence Thereom help please? 17.8.19Question HelpUse the Divergence Theorem to compute the net outward flux of the field F = (x,2y, - z) across the surface S, where S is the boundary of the tetrahedron in the firstoctant formed by the plane x +y +

Consider the vector field F=x,2y,-z. S is the boundary of the tetrahedron in the first octant formed by the plane x+y+z=1. So, the bounds of the region can be written as, 0<x<1, 0<y<1-x, 0<z<1-x-y. Find the value of divF. divF=divx,2y, -z=∂∂xx+∂∂y2y+∂∂z-z=1+2-1=2Find the outward flux of the field . ∫∫SF·dS=∬∫EdivFdV=∫01∫01-x∫01-x-y2dzdydx=2∫01∫01-xz01-x-ydydx=2∫01∫01-x1-x-ydydx=2∫011-xy-y2201-xdx=2∫011-x1-x-1-x22-1dx=∫01x2-2x+1dx=x33-2x22+x01=133-2122+1-0=13-1+1=13 Hence, the net outward flux across the boundary of the tetrahedron is 13.