Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 4 square root x, the y-axis, y=12; about the y-axis

Answer 1

To get limits of integration we solve system y = 4sqrt(x) and y = 12; 4sqrt(x) = 12; sqrt(x) = 3; x = 3² = 9.

Using shelf method volume V = 2π∫₀⁹x(12 - 4sqrt(x))dx = 2π∫₀⁹(12x - 4x^3/2)dx = 2π(6x² - 8/5x^5/2)₀⁹ = 2π·(6·9² - 8/5·9^5/2) = 2π(486 - 388.8) ≈ 610.73

Answer: volume of solid V ≈ 610.73 cubic units