Find the volume of the solid obtained by rotating the region bounded by y=4x and y=2sqrt(x) about the line x=6.

Check the picture below.

so by graphing those two, we get that little section in gray as you see there, now, x = 6  is a vertical line, so we'll have to put the equations in y-terms and this is a washer, so we'll use the washer method.

the way I get the radii is by using the "area under the curve" way, namely, I use it to get R² once and again to get r² and using each time the axis of rotation as one of my functions, in this case the axis of rotation will be f(x), and to get R² will use the "farthest from the axis of rotation" radius, and for r² the "closest to the axis of rotation".

now, both lines if do an equation on where they meet or where one equals the other, we'd get the values for y = 0 and y = 1, not surprisingly in the picture.

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step-by-step explanation: