Volume with Cylindrical shells

Question

Sketch the first quadrant region bounded below by the graph of g(x)=625/(x^2+25)^2,above by f(x)=2−625(x^2+25)^2,and at the right by x=4. Rotating that region about the y-axis generates a solid whose volume is

Answer 1

625/(x² + 25)² = 2 - 625/(x² + 25)²; 625 = (x² + 25)²; x² = 0, x = 0

Volume v = 2π∫₀⁴x[2 - 1250/(x² + 25)²]dx = 2π(x² + 625/(x² + 25))₀⁴ = 2π(16 + 625/41 - 25) = 512π/41