Let R be the region bounded by y=4-x^2 and the x-axis where 0<=x<=2. Use the method of disks and cylindrical shells to find the volume by rotating R about the y-axis

Answer 1

4 - x² = 0; x = 2. By Shells Method V = 2π∫₀²x(4 - x²)dx = 2π(2x² - x⁴/4)₀² = 2π(8 - 4) = 8π

x = √(4 - y); 0 ≤ y ≤ 4; By Disk methodV = π∫₀⁴(4 - y)dy = π(4y - y²/2)₀⁴ = π(16 - 8) = 8π