Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z)=xi-zj+yk S is the part of the sphere x² + y² + z² = 9 in the first octant, with orientation toward the origin

Consider the graph of an ellipse C, oriented counterclockwise. Graphs of the vector fields F,, F,, F, and F, along the curve C are given (see figures). Along C, F, and F, are tangent to C, and F, and F, are normal to C. Determine whether the following integrals are positive, negative, or equal to 0. b. F, · T ds JF T ds а. ·T ds с. C d. F -T ds F -n ds f. F,•n ds е. g. F•n ds h. Fn ds Vectors of F1 along C Vectors of F2 along C Vectors of F3 along C Vectors of F4 along C

Consider the vector field is F = (z, 3x, 5) and the surface S is the positively oriented surface of the portion of z = 9 – x2 – y2 that lies inside x2 + y² = 1. a. Sketch the surface S and the curve of intersection C (I know it's in 3d, but do your best). b. Use Stoke's theorem to calculate F dr.

Answer all parts please