# How do you find the volume of #y=2x^2#; #y=0#; #x=2# revolved about the x axis?

There is a mistake:

See explanation below

The x-axis is the revolution axis, then

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To find the volume of the solid formed by revolving the region bounded by the curves ( y = 2x^2 ), ( y = 0 ), and ( x = 2 ) about the x-axis, you can use the disk method. The formula for the volume using the disk method is ( V = \pi \int_{a}^{b} [f(x)]^2 , dx ), where ( f(x) ) is the outer radius function, and ( a ) and ( b ) are the limits of integration. In this case, ( a = 0 ) and ( b = 2 ), and the outer radius function ( f(x) = 2x^2 ).

Therefore, the volume can be calculated as ( V = \pi \int_{0}^{2} (2x^2)^2 , dx ).

Solving this integral will give you the volume of the solid of revolution.

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