Consider: J²u J²u + = 0, əx² Əy² ди ər u(x,0) = 0, (PDE) (BC1) (BC2) (BC3) u(x, y) remains bounded as y→∞0, 0
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- How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Any help would be greatly appreciated. :)How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help. :)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.
- Evaluate the tiple integral 7xdV, where E is bounded by the paraboloid x=7y2+7z2 and the plane x=7Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)Verify Green’s theorem in the plane for RC(3x2 − 8y2) dx + (4y − 6xy) dy, whereC is the boundary of the region y =√x and y = x2
- The solid bounded by the surfaces S1: −2 (z - 2) = y2 S2: x = 5 - 2z S3: x = 0 S4: y = 0 S5: z = 0 Corresponds to: The graphics are in the attached imageUse Green's Theorem to evaluate the line integral. C y dx + 7x dy C: square with vertices (0, 0), (0, 1), (1, 0), and (1, 1)Evaluate the line integral ∮(−ysin(xy)i−xsin(xy)j)dr using the potential function f(x,y)=cos(xy) where C is any path from (−1,0) to (π/2,1/2).