solve it with proper solution

11. [-/1 Points] DETAILS SESSCALCET2 13.7.028. MY NOTES ASK YOUR TEACHER 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) = xy i + 16x2 j + yz k S is the surface z = xey, 0 s x = 1, 0 sys 4, with upward orientation Need Help? Read ItVA Topic 9 - HW 4: (Stokes' Theorem X + X -> C A webassign.net/web/Student/Assignment-Responses/last?dep=24613345 EXAMPLE 1 Evaluate C F . dr, where F(x, y, z) = -4yzi + 7xj + 322k and C is the curve of the intersection of the plane y + z = 1 and the cylinder x2 + yz = 1. (Orient C to be counterclockwise when viewed from above.) SOLUTION The curve C (an ellipse) is shown in the figure. Although F . dr could be evaluated directly, it's D UL easier to use Stokes' Theorem. We first compute Video Example () curl F = ax -4y 7x 3z2 Although there are many surfaces with boundary C, the most convenient choice is the elliptical region S in the plane y + z = 1 that is bounded by C. If we orient S upwards, then C has the induced positive orientation. The projection D of S on the xy-plane is the disk x2 + y?