(a) To determine Calculate the volume of the solid. Explanation Given information: The solid lies between planes perpendicular to the x axis. The shape of the cross section is isosceles triangles of height 6. The base of the solid is the region bounded by the graphs of y = x and y = x 2 . Definition used: The volume of a solid of integrable cross-sectional area A ( x ) from x = a to x = b is the integral of A from a to b , V = ∫ a b A ( x ) d x Calculation: The base of the solid is x − x 2 . Calculate the cross sectional area A ( x ) as follows: A ( x ) = 1 2 ( base ) ( height ) Substitute x − x 2 for base and 6 for height. A ( x ) = 1 2 ( x − x 2 ) 6 = 3 x − 3 x 2 Calculate the volume of the solid using the formula: V = (b) To determine Calculate the volume of the solid.

4th Edition

ISBN: 9780134439099

Author: Hass, Joel., Heil, Christopher , WEIR, Maurice D.

Publisher: Pearson,

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Chapter 6.1, Problem 8E

(a)

To determine

Calculate the volume of the solid.

(b)

To determine

Calculate the volume of the solid.

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Chapter 6.1, Problem 7E

Chapter 6.1, Problem 9E

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