Use Stokes' Theorem to evaluate S (double integral) curl F · dS. F(x, y, z) = x^2*y^3*z i + sin(xyz) j + xyz k, S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
Use Stokes' Theorem to evaluate S (double integral) curl F · dS. F(x, y, z) = x^2*y^3*z i + sin(xyz) j + xyz k, S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y =...
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.
3. Use Stokes' Theorem to evaluate [ſcurl Ē. d5 where F(x, y, z)= x?y?zi + sin(xyz)ị + xyzk, o is the portion of the cone y² = x² +z? that lies between the planes y=0) and y = 3, oriented in the direction of the positive y-axis. [2187 1/4]
ie Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x2 sin(z)i + y2 + xyk, S is the part of the paraboloid z = upward. - x2 - y2 that lies above the xy-plane, oriented
Use Stokes' Theorem to evaluate sta curl F. ds. F(x, y, z) = xyzi + xyj + x2yzk, S consists of the top and four sides (but not the bottom of the cube with vertices (+3, +3, +3), oriented outward. Need Help? Read It Watch It Talk to a Tutor Submit Answer 33. [-/2.5 Points] DETAILS SCALC8 16.8.018. MY NOTES ASK YOUR Evaluate le (y + 5 sin(x)) dx + (z2 + 3 cos(y)) dy + x3 dz where C...
Evaluate the Surface Integral, double integral F*ds, where F = [(e^x)cos(yz), (x^2)y, (z^2)(e^2x)] and S is a part of the cylinder 4y^2 + z^2 =4 that lies above the xy plane and between x=0 and x=2 with upward orientation (oriented in the direction of the positive z-axis). ASAP PLEASE
Use Stokes' Theorem to evaluate. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented upward. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented...
Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 5yzi + 9x j +2yze+'k ,S is the portion of the paraboloid z = x2 + aby2 for 0 sz s 3, and the unit normal on S points away from the z-axis. 16 Enter your answer symbolically, as in these examples
Evaluate the line integral in Stokes Theorem to evaluate the surface integral J J(VxF)-n ds. Assume that n points in an upward direction F (xty,y z,z+x) S is the tilted disk enclosed by r()-(3 cost,4sint,7 cos t Rewrite the surface integral as a line integral. Use increasing limits of integration. dt (Type exact answers, using π as needed.) Find the value of the surface integral. JÍs×F).nds-ロ (Type an exact answer, using π as needed.) Evaluate the line integral in Stokes...
4. Consider the vector field A - (x - 322)i [3 sin(xyz)]j - 3ry2 k. Use Stokes' theorem to calculate where S is the surface of the cone z 1-VT2 + y2 above the TU plane. 4. Consider the vector field A - (x - 322)i [3 sin(xyz)]j - 3ry2 k. Use Stokes' theorem to calculate where S is the surface of the cone z 1-VT2 + y2 above the TU plane.
. Problem #8: Use Stokes' Theorem to evaluate | F• dr where F = (x + 52)i + (6x + y)j + (7y - -)k and C is the curve of intersection of the plane x + 3y += = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) Problem #8: Just Save Submit Problem #8 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #8 Your Answer: Your Mark:...