Find the volume of a solid

Question

Find the volume of the solid obtained by rotating the region bounded by y=x and y=x^4 about the x-axis

Answer 1

This calls for the washer method, with y = x⁴ lying below y = x until they intersect at x = 1. Washer area = πx² - πx⁸ and each volume element is A•dx, so V = π ∫₀¹ (x² - x⁸) dx = π [x³/3 - x⁹/9]₀¹ = π (1/3 - 1/9) = 2/9 π.