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IntegralProblems

# IntegralProblems - where is the circle in the plane...

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1. Evaluate the line integral where is the curve given by and with 2. Evaluate the line integral where is the curve given by with 3. Evaluate the line integral where is the quarter-circle from to 4. Find the work done by the force field on any object moving along the curve where is the path given by and for 5. Find the surface area of the surface of the portion of the paraboloid that lies inside the cylinder 6. Find the surface area of the surface of the portion of the cone inside the cylinder 7. Evaluate the surface integral with 8. Evaluate the surface integral with where 9. Evaluate (flux of F through surface S) where and is the surface of the cube bounded by the planes and

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10. Evaluate the surface integral where is the surface determined by with 11. Evaluate (flux of F through surface S) where and is the surface of the portion of the plane that lies inside the cylinder 12. Use Stokes' theorem to evaluate the line integral (circulation around curve C)
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Unformatted text preview: where is the circle in the plane counterclockwise when viewed from above the origin. 13. Use Stokes' theorem to evaluate (flux of curl F through surface S) where and is the part of the cube and except for the face where 14. Use the divergence theorem to evaluate the surface integral (flux of F through surface S) for the vector function and closed boundary surface given by the sphere 15. Use the divergence theorem to evaluate the surface integral (flux of F through surface S) for the vector function and closed boundary surface given by the solid bounded by the cylinder and the planes and 16. (Optional) Use the divergence theorem to evaluate the surface integral(flux of F through surface S) for the vector function and closed boundary surface given by the five faces of the unit cube, and missing and where is the unit normal vector pointing away from the origin....
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