Explanation Given: z = 9 − x 3 , y = − x 2 + 2 , y = 0 , z = 0 , x ≥ 0 Formula used: Volume of the solid region Q is V = ∭ Q d x d y d z Calculation: From the given equations, z varies from 0 to 9 − x 3 , y varies from 0 to − x 2 + 2 and x varies from 0 to 2 . Hence, the volume of the solid is given by, ∫ 0 2 ∫ 0 − x 2 + 2 ∫ 0 9 − x 3 d z d y d x = ∫ 0 2 ∫ 0 − x 2 + 2 [ z ] 0 9 − x 3 d y d x = ∫ 0 2 ∫ 0 3 − 3 x ( 9 − x 3 ) d y d x = ∫ 0 2 [ ( 9 − x 3 ) y ] 0 3 − 3 x d x

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Chapter 14.6, Problem 22E

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To calculate: The volume of the solid bounded by the graphs of equations z=9−x3, y=−x2+2, y=0, z=0, x≥0 using triple integral.

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Chapter 14.6, Problem 21E

Chapter 14.6, Problem 23E

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Chapter 14 Solutions

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The volume of the solid bounded by the graphs of equations z = 9 − x 3 , y = − x 2 + 2 , y = 0 , z = 0 , x ≥ 0 using triple integral.

Solution Summary: The author calculates the volume of the solid bounded by the graphs of equations z=9-x3, y=0, and x = 0.

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To calculate: The volume of the solid bounded by the graphs of equations z=9−x3, y=−x2+2, y=0, z=0, x≥0 using triple integral.

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Chapter 14 Solutions