Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

The domain bounded by the curves y = x^{2} and x = y^{2} can be described by the inequalities:

0 ≤ y ≤ 1, y^{2} ≤ x ≤ √(y). Then the volume can be expressed as the following integral:

V = π ∫_{0}^{1} [x_{2}^{2}(y) – x_{1}^{2}(y)] dy, where x_{2}(y) = √(y) + 5 and x_{1}(y) = y^{2} + 5.

Thus, V = π ∫_{0}^{1} [(√(y) + 5)^{2} – ( y^{2} + 5)^{2}] dy =

π ∫_{0}^{1} [(y + 10√(y) + 25) – (y^{4} + 10y^{2} + 25)] dy =

π ∫_{0}^{1} [y + 10√(y) – y^{4} – 10y^{2} ] dy =

π ( y^{2}/2 + (20/3)y√(y) – y^{5}/5 – (10/3)y^{3 })]_{0}^{1} =

π ( 1/2 + 20/3 – 1/5 – 10/3) = π ( 1/2 + 10/3 – 1/5) = π ( 15 + 100 – 6)/30 = 109π/30.

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