Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x^2, y = 18 − x^2; about the x-axis

Answer 1

Answer 2

Limits of intgration: 18 - x² = x²; 2x² = 9; x = ±3;

V = π∫_-3³[(18 - x²)² - (x²)²]dx = 2π∫₀³(324 - 36x²)dx = 2π(324x - 12x³)₀³ = 1296π = 4071.5