Use a double integral to find the solid bounded by z = 1 - y^2 and z = y^2 -1 for 0 < x < 2

1
by sweetysiri92
where is the given series? question lacks data
In place of previous question I posted another one
Dont know
i am telling that the answer is 16/3. the limits of integration are -1 to 1. please see, I modified.

2014-10-15T15:37:09+05:30

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In the y-z plane, the curve z = 1 - y² and the curve z = y² - 1 form a bounded area around y axis. It is symmetric wrt y axis. The shape of curve is parabolic.

In the y-z plane the intersection of z = 1 - y
² and z = y² - 1 gives the limits of integration and define the bounded area.

z = 1 - y
² = y² - 1       =>    2 y² = 2      =>  y = +1 or  -1

So the cross section area is bounded between  y = -1 and y = +1.

In the x-axis direction the solid has a uniform area.  So the solid is a cylinder with the length in the x direction with cross section in the y-z plane.

Volume = cross sectional area * length

thanx n u r welcom