8. (10 points) Use Stokes' Theorem to evaluate where (..) - (awy, 3) and C is...
is the Use Stokes' theorem to evaluate ſc(1+y)z dx + (1+z)x dy+(1 + x)y dz, where counterclockwise-oriented triangle with vertices (1,0,0), (0,1,0), and (0,0,1).
Let Ě = < 2x + y², 8y + z2, 6z + x2 >. Use Stokes' Theorem to evaluate so F. dri where C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1), oriented counterclockwise as viewed from above.
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
4. Use Stokes' Theorem to evaluate Fodr where F =x' i -4:+ xy k and Cis is the circle of radius 1 at x = -3 and perpendicular to the x-axis. Chas a counter clockwise rotation if you are looking down the x-axis from the positive x-axis to the negative x-axis. See the figure below for a sketch of the curve.
Use Stokes' Theorem to evaluate les F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (3, 0, 0), (0, 3,0), and (0, 0, 3). Need Help? Read it Watch It Master It Talk to a Tutor
please solve this question. answer is 15pi/ √2. please don't make mistakes. I am sending you guys correct answers , but still you are making mistakes and getting other answers. 28. Use Stokes Theorem to evaluateF dr. where C is the circle22 in the ry-plane with counterclockwise orientation looking down the positive z-axis. 28. Use Stokes Theorem to evaluateF dr. where C is the circle22 in the ry-plane with counterclockwise orientation looking down the positive z-axis.
14. (10 pts) Use Stokes' Theorem to compute F dr where F , y,) 32,5x, -2yand the curve C is given by the triangle with vertices (0,2,0), (3,0,0), and (0,0, 1) with positive orientation 14. (10 pts) Use Stokes' Theorem to compute F dr where F , y,) 32,5x, -2yand the curve C is given by the triangle with vertices (0,2,0), (3,0,0), and (0,0, 1) with positive orientation
Use Stokes' Theorem to evaluate fe(x+y)dx + (2x – 3)dy +(y +z)dz over the boundary of the triangle with vertices (2,0,0), (0,3,0), (0,0,6) traversed in the counter clockwise direction.
3) Given vector field F(x,y,z)=<y, xz,x? >. Find N dr where T is the path around the triangle with vertices (1,0,0),(0,1,0) and (0,0,1) traced counterclockwise (when viewed from above.)
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...