Find the volume of a solid whose base is bounded by the parabola x=y^2 and the line x=9, having square cross-sections when sliced perpendicular to the x-axis.

Answer 1

the square has base 2y=2√x and height 2y=2√x and thickness dx

So,

v = ∫[0,9] (2√x)(2√x) dx
= ∫[0,9] 4x dx

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