Find y dv, where E' is the solid bounded by the parabolic cylinder z = ? and z=13-3y. Round your answer to four decimal places. ² and the planes y = 0
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- Use cylindrical coordinates to evaluate the triple integral ∫∫∫E √(x2+y2)dV, where E is the solid bounded by the circular paraboloid z=16−16(x2+y2) and the xy -plane.Given F = xi - yj, find the value of ∬F • n dS over the closed surface bounded by the planes z = 0, z = 1, and the cylinder x2 + y2 = a2, where n is the unit outward normal, by direct calculation. (Hint: The element of area is dS = a dθ dz in cylindrical coordinates on the curved surface.)Use cylindrical coordinates to evaluate the triple integral ∫∫∫E x^2 dV, where E is the solid that lies within the cylinder x^2+y^2=4, above the plane z=0, and below the cone z^2=25x^2+25y^2.