find the volume of the region bounded by y2x2 yxx0 and the y

find the volume of the region bounded by y=2-x^2, y=x(x>0) and the y axis revolved around x=-1

a) Find where curve x = y^2 and line x = 1 intersect y² = 1 y = ±1 Use disk method, where each cross-section perpendicular to axis x=1 has radius r = 1 - y² V = p ??1¹ r² dy V = p ??1¹ (1 - y²)² dy V = p ??1¹ (1 - 2y² + y4) dy V = p (y - 2y³/3 + y5/5) |?1¹ V = p ((1 - 2/3 + 1/5) - (-1 + 2/3 - 1/5)) V = p ((8/15) - (-8/15)) V = 16p/15