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Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone if its density function is

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Use Stokes' Theorem to evaluate where is the curve of intersection of the plane and the cylinder is oriented counterclockwise as viewed from above.

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Set up, but do not evaluate, a double integral for the area of the surface with parametric equations

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Use Stoke's theorem to evaluate C is the curve of intersection of the plane z = x + 9 and the cylinder

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The temperature at the point in a substance with conductivity is Find the rate of heat flow inward across the cylindrical

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Use a computer algebra system to compute the flux of F across S. S is the surface of the cube cut from the first octant by the planes

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Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find , where a is the constant vector.

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Suppose that where g is a function of one variable such that .Evaluate where S is the sphere

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Evaluate the surface integral for the given vector field F and the oriented surface S. In other words, find the flux of F across S.

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Find an equation of the tangent plane to the parametric surface represented by r at the specified point. ;

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Use Gauss's Law to find the charge contained in the solid hemisphere , if the electric field is

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Evaluate the surface integral for the given vector field F and the oriented surface S. In other words, find the flux of F across S. in the first octant, with orientation toward the origin.

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Use Stokes' Theorem to evaluate where and is the triangle with vertices is oriented counterclockwise as viewed from above.

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Use Stokes' Theorem to evaluate is the part of the paraboloid that lies inside the cylinder oriented upword.

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Use Stokes' Theorem to evaluate where is the circle . is oriented counterclockwise as viewed from above.

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Evaluate the surface integral. Round your answer to four decimal places. S is surface

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Evaluate the surface integral. S is the part of the plane that lies in the first octant.

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A fluid with density flows with velocity Find the rate of flow upward through the paraboloid

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Use the Divergence Theorem to calculate the surface integral ; that is, calculate the flux of across . S is the surface of the box bounded by the coordinate planes and the planes .

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