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- An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two fixed points called _____ is a constant.Calculate ⌠⌠F*dS if F(x,y,z)=x^2ye^zi + xy^2j-2xye^zk where S is the surface of the box bounded by the coordinate planes and the planes x=4 y=3 z=2Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the coordinate planes and the planes x = 2 and y + z = 1.
- integrate ƒ over the given region.Quadrilateral ƒ(x, y) = x>y over the region in the first quadrantbounded by the lines y = x, y = 2x, x = 1, and x = 2Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x = 1, y = 1, and z = 1Show that if f(x, y) is homogeneous of degree n, then xfx(x, y) + yfy(x, y) = nf(x, y).
- C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0, −10), directed counter-clockwise. Evaluate integralC (3y/(x^2+y^2) dx − 3x/(x^ 2 + y^2) dy)Find all planes in R3 whose intersection with the xy-plane is the liner( t) = t ( 2, 1, 0) .Let F(x, y) = 2x 2yi + 3xyj, and C be the boundary of the square with corner points (±1, ±1), positively oriented. Find the flux of F across C.
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