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Unformatted text preview: Version 058 – DGQ11 – gilbert – (55485) 1 This print-out should have 3 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The solid shown in z y x is bounded by the paraboloid z = 3- x 2- y 2 , and the coordinates planes as well as the planes x = 1 , y = 1 . Find the volume of this solid. 1. volume = 11 3 2. volume = 8 3 3. volume = 3 4. volume = 10 3 5. volume = 7 3 correct Explanation: The volume of the solid is given by the double integral V = integraldisplay integraldisplay D z dxdy = integraldisplay integraldisplay D (3- x 2- y 2 ) dxdy where D is its base as a region in the xy-plane. Now D is the rectangular region in the xy- plane enclosed by the x- and y-axes as well the lines x = 1 and y = 1 shown as the shaded region in 1 1 x y Thus if we integrate first with respect to y for fixed x along the solid vertical line and then with respect to x , the volume is given by V = integraldisplay 1 parenleftBig...
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- Spring '07
- dy dx, dx, xyey dx dy