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Ankita Asked a Question July 23, 2020 12:06 pm 30 pts - CSIR NET
- Physical Sciences

STaT. Ttah + 27ta-n EvaluateJJ.F.ds, where F- zi +xj - 3yzk and S is the surface of the cylinder x* + y = 16 included in the first octant between z = 0 and z = 5 A unit vector normal to the surface S(x? + y = 16) is ol. -_2xi 2xi+2yj 4x+4y) xi +yi 4 We have JFids-f F dk dz 2 where R is the projection of S on the x-z plane. It should be noted that in this case we cannot take the projection of S on the x-y plane as the surface S is perpendicular to the x-y plane. Now, Fi-(zi+x-3y'zk) i (xZ+ Xy) 4 herefore, the required surface integral is XZ + Xy dx dz l-4va XZ =+x dx dz = 90 4 y/4 z-0Jx-016-x

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