4. Use the Divergence Theorem to evaluate the flux integral JS, F-ndA over the surface of a rectangular parallelepiped with dimensions 2 × 3 × 1 units if F = (3x²y³5,3y, -xy³ 26).
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Please solve the flux
Step by step
Solved in 3 steps
- Verify Formula (1) in the Divergence Theorem by evaluatingthe surface integral and the triple integral. 1. F(x, y, z) = xi + y j + zk; σ is the surface of the cubebounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0,z = 1.Verify the divergence theorem for A = 2xyi -yz 2 j + xzk taken over the regionbounded by x = 0, y =0, z = 0 , x = 2, y = 1 and z = 3.use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the region cut from the first octant by the plane y+z=4 and the elliptical cylinder 4x^2+y^2=16
- Use the Divergence Theorem to evaluate the flux of F = yi - xj + 2xk across the sphere x ^ 2 + y ^ 2 + z ^ 2 = 25 with outward orientation . Flux of FUse divergence theorem to find the volume of quadric surface z² + 3y + 4x² = 3 with the solid region bounded by the xy-plane and y = -2. Let F = xzi + 3yzj +x²k.Use Divergence Theorem to evaluate the flux integral∫∫F·ndS, where F = 〈x^2, y^2, z^2〉,S is the sphere x^2+ y^2+ z^2= 25.
- Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of the region cut from the first octant by the plane y + z = 4 and the elliptical cylinder 4x2 + y2 = 16.Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of the region cut from the first octant by the plane y + z = 4 and the elliptical cylinder 4x2 + y2 = 16S is the region bounded by paraboloid z=9-x^2-y^2 and the xy plane
- Compute the moments of the semicircle x2 + y2 = R2, y ≥ 0 as line integrals. Verify that the centroid is (0,4R/(3π)).use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i - 2xyj + 3xzk D: The region cut from the first octant by the sphere x2 + y2 + z2 = 4.