Find the volume of the solid generated by revolving the region bounded by the parabola y=-x^2/4 and the line y=-1 about the following lines: a.) y=-1 b.)y=-2 c.)y=1

Question

Find the volume of the solid generated by revolving the region bounded by the parabola y=-x^2/4 and the line y=-1 about the following lines: a.) y=-1 b.)y=-2 c.)y=1

Answer 1

Answer 2

-1 = - x²/4; x = ± 2;∫

a) v = π∫_-2²(1 - x⁴/16)dx = 2π(x - x⁵/80)₀² = 3.2π

b) v = π∫_-2²[(2 - x²/4)² - 1²]dx = 112π/15

c) v = π ∫_-2²[2² - (1 + x²/4)²]dx = 128π/15