Math 226 SI Midterm 2 Review

4 convert the following integral to cylindrical

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Unformatted text preview: . 4. Convert the following integral to cylindrical coordinates and then evaluate: √ ∫∫ ∫ √ 5. Calculate the volume below the spherical surface surface √ ( ) and above the conical . 6. Consider the tetrahedron with corners at (0; 0; 0), (a; a; 0), (0; a; 0), and (0; 0; a), with density: ( ) ( ) where is a constant. Calculate the total mass m. 7. Compute the Jacobian for the following change of variables : 8. a. Evaluate the line integral ∫ where C is the counterclockwise oriented triangle with vertices (0,0), (0,2), and (2,2) and (...
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