Applications of Integration

Question

The region between the graphs of x=y^2 and x=2y is rotated around the line y=2.

The volume of the resulting solid is:

Answer 1

Limits of integration: x = (x/2)²; x = 0 or x = 4; By disk/washer method volume V = π∫₀⁴[(2 - x/2)² - (2 - √x)²]dx = π∫₀⁴(x²/4 - 2x + 4√x)dx = π(x³/12 - x² + 8/3x^3/2)₀⁴ = π(16/3 - 16 + 8/3·8) = 32π/3 = 33.51