Applications of Integration

Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves x=y² and x=1 about the line x=1.

Volume =

Answer 1

Limits of integration: 1 = y², y = ±1.

By disk/washer method volume V = π∫_-1¹(1 - y²)²dy = 2π∫₀¹(1 - 2y² + y⁴)dy = 2π∫₀¹(y - 2y³/3 + y⁵/5)₀¹ =

2π(1 - 2/3 + 1/5) = 16π/15 = 3.351