ha lvh262 Homework 15 1 karakurt 56295 This print out should have 3 questions Multiple choice questions may continue on the next column or page find all choices before answering 001 1 The graph of the function z f x y 3 x is the plane shown in 10 0 points Evaluate the double integral Z Z I 6 dxdy z A y with n o A x y 2 x 6 2 y 5 by first identifying it as the volume of a solid 3 x 1 I 76 Determine the value of the double integral Z Z I f x y dxdy 2 I 74 3 I 78 A 4 I 72 correct 5 I 80 Explanation The value of I is the volume of the solid below the graph of z f x y 6 and above the region n o A x y 2 x 6 2 y 5 Since A is a rectangle this solid is a box with base A and height 6 Its volume therefore is given by length width height 6 2 5 2 6 Consequently I 72 over the region n o A x y 0 x 3 0 y 2 in the xy plane by first identifying it as the volume of a solid below the graph of f 1 I 11 cu units 2 I 10 cu units 3 I 12 cu units 4 I 9 cu units correct 5 I 13 cu units Explanation The double integral Z Z I f x y dxdy A keywords volume double integral rectangular region rectangular solid 002 10 0 points is the volume of the solid below the graph of f having the rectangle n o A x y 0 x 3 0 y 2 ha lvh262 Homework 15 1 karakurt 56295 for its base Thus the solid is the wedge 2 having the rectangle R x y 4 x 6 0 y 2 z as its base Thus the solid is the wedge 3 z y y 3 2 3 and so its volume is the area of triangular face multiplied by the thickness of the wedge Consequently I 9 cu units keywords double integral linear function volume under graph volume rectangular region prism triangle 003 10 0 points Determine the value of the double integral Z Z I 6 x dxdy R over the region R x y 4 x 6 0 y 2 in the xy plane by first identifying it as the volume of a solid 1 I 3 2 I 6 3 I 4 correct 4 I 5 5 I 2 Explanation The double integral I is the volume of the solid below the graph of z 6 x 6 2 x 2 6 x having a triangular face of height 2 and base 2 Since the wedge has length 2 the solid thus has volume 4 keywords
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