Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^2 , y = 1 , and the y -axis and whose cross-sections perpendicular to the x axis are squares.

Answer 1

Volume V = ∫₀¹(1 - x²)²dx = (x - 2x³/3 + x⁵/5)₀¹ = 1 - 2/3 + 1/5 = 8/15;

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