Applications of Integrals

First of all, the line of integration is x + y = 1. Therefore, when a disc in orientation with respective to the line, we have dx = dy (in magnitude) and we may let the thickness of the disc be ds where ds = dx√2
Also, in terms of x only, the coordinates of the point on the curve can be expressed as [x, (1 - √x)2].
So the volume of revolution can be found as follows:

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