Find the volume of the solid generated by revolving

Question

Find the volume of the solid generated by revolving the following region about the​ y-axis.The region in the first quadrant bounded above by the parabola y=x²​, below by the​ x-axis, and on the right by the line x=1.

Find Volume?

Answer 1

2π∫₀¹x²dx = 2π(1/3)|₀¹=2π/3

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Answer 2

By shell method volume v = 2π∫₀x·x²dx = = πx⁴/2₀¹ = π/2 = 1.571