Explanation Given: For graph refer to the book Calculation: The two provided equations are: z = x 2 + y 2 and z = 2 x First find the intersection of these two surfaces by equating them. x 2 + y 2 = 2 x x 2 + y 2 − 2 x = 0 x 2 − 2 x + 1 + y 2 = 1 ( x − 1 ) 2 + y 2 = 1 This is an equation of circle having centre at ( 1 , 0 ) . The volume of a solid region is provided by, Volume = (volume under paraboloid) − (volume under plane) V = ∫ 0 2 ∫ − 1 − ( x − 1 ) 2 1 − ( x − 1 ) 2 ( x 2 + y 2 ) d y d x − ∫

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Chapter 14.2, Problem 34E

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To calculate: The double integral setup to find the volume of the solid region bounded by the graphs of the equations.

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Chapter 14.2, Problem 33E

Chapter 14.2, Problem 35E

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Chapter 14 Solutions

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The double integral setup to find the volume of the solid region bounded by the graphs of the equations.

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Chapter 14 Solutions