Question
Asked Sep 11, 2019
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Find the volume V of the described solid S.

The base of S is the region enclosed by the parabola 
y = 3 − 2x2
 and the x−axis. Cross-sections perpendicular to the y−axis are squares.
 
V=?
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Expert Answer

Step 1

Given base of the solid S enclosed by parabola y=3-2x2 and the x axis and cross-sections are perpendicular to the y axis are squares. So first find the cross-sectional area of solid and then integrate it along y axis to find the volume.

Step 2

Cross-sectional area is in the form of Squares with side 2x and width dx is given by

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A(x) (2x)2 A(x) 4x As y 3-2x2 (3-y A(x) 4 2

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Step 3

For limit of integration along y axis, put x=0 we get y=3 and also y is bounded below by ...

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Image Transcriptionclose

dy dv 43-y 2 3 3- y 4 sav dy 2 V 2 (3-y)dy V 2 3y 2 l0 V 29 2 V 9

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