What is the volume of the solid of revolution formed when the region in quadrant l bounded by f(x)=x^2 and g(x)=4x is revolved about the x-axis? (Show your integral in your answer)

Answer 1

The function y = 4x is the outside radius and the function y = x² is the inside radius of a washer cross-section that can be integrated from x = 0 to x =4

V = ∫A(x)dx = ₀ ∫⁴ π(r_o² - r_i²)dx = ₀ ∫⁴ π[(4x)² - (x²)]dx = 2048π/15 ≈ 428.9 units³