Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x = 0 , y = 1 , x = y^6 , about the line y = 1 .

Question

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Answer 1

USING CYLINDRICAL SHELLS

Volume = ∫_y=0^y=1[ 2π(1-y) y⁶]dy = π/28 cubic units

USING THE WASHER METHOD

Volume = ∫_x=0^x=1[π{x^(1/6) -1}²]dx = π/28 cubic units

Answer 2

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