MAT 307 Final: MAT 307 SBU Fall 12 Final
31 Jan 2019
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Do all of your work on these pages and cross out any work that should be ignored. Use the backs of pages if needed, indicating where you"ve done this. Notes, books, calculators and discussions with others are not permitted: (15pts) evaluate the integral where d is the domain 0 x 1, y x2 and y x in r2. 2: (20pts) find the volume of the region bounded by or between the paraboloids z = x2 + y2 and z = 36 3x2 3y2. State stokes" theorem for surface integrals in r3. (b). Verify stokes" theorem is true for the surface s equal to the part of the paraboloid z = x2 + y2 with 0 z 4 and vector eld v = ( y, x, z2). 4: (20pts) suppose r is a smooth bounded region in r3 with boundary r a smooth closed surface.
