Explanation The solid region is bounded by the coordinate planes and the plane z = 5 − x − y , and lies in the first octant. So, the region is bounded by the planes x = 0 , y = 0 , z = 0 and z = 5 − x − y . Now find intercepts on the axis for the plane, z = 5 − x − y x -intercept is, z = 5 − x − y 0 = 5 − x − 0 x = 5 y -intercept is, z = 5 − x − y 0 = 5 − 0 − y y = 5 And z -intercept is, z = 5 − x − y z = 5 − 0 − 0 z = 5 So, the solid region formed is shown in the below figure,

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Chapter 14.6, Problem 11E

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The triple integral form for the volume of the solid in the first octant bounded by the coordinate planes and the plane z=5−x−y.

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Chapter 14.6, Problem 10E

Chapter 14.6, Problem 12E

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The triple integral form for the volume of the solid in the first octant bounded by the coordinate planes and the plane z = 5 − x − y .

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The triple integral form for the volume of the solid in the first octant bounded by the coordinate planes and the plane z=5−x−y.

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