If F=xyi+yzj+xz, use Stokes's theorem to evaluate o∫F.drwhere the surface is given by z=6-2x-3y for0≤x≤3;0≤y≤2 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Question: 2. (7 pts) Let F(x, y, z) = xyi+2zj - 2yk and let C be the intersection of plane x+z = 5 and cylinder c2 + y2 = 9, which is oriented counterclockwise when viewed from the top.

F(x,y,z)= xyi + yzj + zxk, C is the boundary of the part of the parabolid z = 1-x^2-y^2, in the first octant, use stoke's therom to evalue integral F*dr Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Question: Suppose F(x, y) = xyi + (x - y)j and C is the triangle from (3, 0) to (-3, 0) to (0, 3) to (3, 0). (a) Find the line integral of F along each segment of the trian

Question: Suppose F?(x,y)=-xyi? +y2j? . (a) Find a vector parametric equation for the parabola y=x2 from the origin to the point (2,4) using t as a parameter.

1 Verify Stokes' theorem for the field v = xyi+yzj where S is the surface of the cube 0<x< 1, 0 <y <1,0 <z< 1 and the face z = 0 is open. 2 If y = 3x?i + xyzj – 5zk verify Stokes' theorem where S is the surface of the cube 0<x< 1, 0 <y <1,0 <z< 1 and the face z = 0 is open. 3 Suppose v = x’i – 3x?y?z?j + (7x +z)k and S is the surface of a cube of side 2 units lying in the region 0 < x ...

Question: Given F(x,y)=(1 + xy)e^xyi + x^2e^xyj (a) Show that F is conservative. (b) Find a function f such that F = delf (c) Use part (b) to evaluate integral F * dr where C is the curve with equation r(t) = costi + 2sintj 0 <= t <= 2 [Hint: Fundamental Theorem of Line Integrals].

Answer to Find the work done by the force F=xyi+(y−x)j over

Question: If phi = 2xyz^2, F rightarrow = xyi^- zj^+ x^2k^and C is the curve x = t^2, y = 2t, z = t^3 from t = 0 to t = 2, evaluate the line integrals integral_C phi dr rightarrow, integral F rightarrow times dr rightarrow.

In this problem you are given a force F = xyî + 2yĵ and you need to compute: (a) √x F (b) The work done by F from (0,0) to (1,3) on Path 1 given by y = 3x².