Given the following vector field and oriented curve C, evaluate F.T ds. F = (-6y,6x) on...
Help Given the following vector field and orientated curve C, evaluate • SF.Tds. c F= (x,y) on the curve r(t) = (12,612), for 1sts3 (x² + y2) 312 The value of the line integral of F over C is (Type an exact answer, using radicals as needed.)
Evaluate the surface integral F dot 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. 24. F(x, y, z) = -xi - yj + z’k, S is the part of the cone z = x2 + y2 between the planes z 1 and 2 3 with downward orientation
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
please help me answer all 4, I need help. thank you Athin wire represented by the smooth curve C with a density (units of mass per longth) has a mass M ds. Find the mass of the wire c {xyxy=4x?, Os 55) with density px.y)-6+3xy. The mass of the wro is about (Round to one decimal place as needed.) Given the force field F, find the work required to move an object on the given oriented curve. F = (y....
Evaluate the surface integral S 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) = xzey i − xzey j + z k S is the part of the plane x + y + z = 7 in the first octant and has upward orientation.
Evaluate the surface integral S 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) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin
Evaluate the surface integralF 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. S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y O and x y 3 Evaluate the surface integralF F ds for the given vector field F and the oriented surface S. In other words, find the...
Let Ě =< 2x + 2,3y+z, 6x + 6y > be a vector field in R3. Evaluate the following surface integral directly: xdA || i-dš= $ 8. (XFL) S Where S is the part of the plane 2x + 3y + z = 6 in the first octant (with upward orientation). SHOW ALL OF YOUR WORK!
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 dlosed surfaces, use the positive (outward) orientation F(x, y, 2) _ yj-zk, sconsists ofthe paraboloid γ_x2 +22, O sys1, and the disk x2 +22 s 1.7-1. Need Help? to Tter Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the...
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 yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...