Revolutionary solid

Calculus Level 3

Let RR be a positive real number. Let the region bounded by y=x y = \sqrt{x} , x=R2x=R^2 and the x-axis be denoted as SS. The volume of the solid obtained by rotating SS about the y-axis is equal to αRβπ \alpha R^\beta \pi. What is α+β? \alpha + \beta ?

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