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2. Let S be the interior of the triangle with vertices (0,0,0), (1,0,0) and (0,1,0). a)...
9. Let S be the triangle below with vertices (0,1,0), (1,0,0) and (0,0,1). (For all three of these points x+y+z=1) Let F =(x+y+z)i + (x + y)] +xk. Set up an integral in dy and dx that will calculate the flux of F through S.
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b. Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
Calculate the volume integral of the function T=z^2 over the tetrahedron with corners (0,0,0), (1,0,0), (0,1,0), and(0,0,1). Can the answer be in-depth please.
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f : R3 +R be the function defined by f(x, y, z) = 1 - 2y + 3z. Using the change of variables theorem, rewrite Is f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
(1 point) Set up a double integral for calculating the flux of F -4xi + yj + zk through the part of the surface z =-2x-4y + 4 above the triangle in the xy-plane with vertices (0,0), (0,4), and (2,0), oriented upward. Instructions: Please enter the integrand in the first answer box. Depending on the order of integration you choose, enter dx and dy in either order into the second and third answer boxes with only one dx or dy...
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 → R be the function defined by f(x, y, z) = 1 - 2y + 32. Using the change of variables theorem, rewrite Ss f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral (8 points).
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1, 2, 3), and (-1,0,1). Let f: R3 R be the function defined by f(x,y, x) = x - 2y + 3z. Using the change of variables theorem, rewrite Ssf as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
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).
6. Let S be the triangle with vertices (0,0,0), (1,0,1), and (1,1,2), ori- ented upward. Calculate the surface integral ,4,5). ds.
Don't give the same solution. Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 +R be the function defined by f(x, y, z) = 2 - 2y + 3z. Using the change of variables theorem, rewrite Js f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral