Calculus Early Transcendentals

Mathematics

Quiz 12 :

Multiple Integrals

Quiz 12 :

Multiple Integrals

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Find the center of mass of a homogeneous solid bounded by the paraboloid img and img
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img

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Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate img where E lies above the paraboloid img and below the plane img .
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E

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Use the transformation img to evaluate the integral img , where R is the region bounded by the ellipse img .
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C

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Find the mass of the solid S bounded by the paraboloid img and the plane img if S has constant density 3.
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Find the Jacobian of the transformation. img
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Use cylindrical coordinates to evaluate the triple integral img where E is the solid that lies between the cylinders img and img above the xy-plane and below the plane img .
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Use a triple integral to find the volume of the solid bounded by img and the planes img and img .
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Find the Jacobian of the transformation. img
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Use the given transformation to evaluate the integral. img , where R is the region in the first quadrant bounded by the lines img and the hyperbolas img .
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Identify the surface with equation img
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Identify the surface with equation img
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Use cylindrical coordinates to evaluate img where T is the solid bounded by the cylinder img and the planes img and img
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Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.
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Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places. img R is the parallelogram bounded by the lines img .
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Calculate the iterated integral. img
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Use spherical coordinates to find the volume of the solid that lies within the sphere img above the xy-plane and below the cone img . Round the answer to two decimal places.
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Use the given transformation to evaluate the integral. img , where R is the square with vertices (0, 0), (4, 6), (6, img ), (10, 2) and img
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Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius img and density 1 about a diameter of its base.
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Use spherical coordinates.Evaluate img , where img is the ball with center the origin and radius img .
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Use cylindrical coordinates to evaluate img
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