y x y x4SolutionA ring would be formed with outer surface

Solution

A ring would be formed with outer surface formed by rotation of y = x and inner from other equation.
Both the equation intersect at x = 0 and 1. and shifting the origin to (0, -1) makes new y = y_old + 1
Volume of small ring, dV = ((x+1)^2 - (x^4 + 1)^2)dx = (-x^8 - 2x^4 + x^2 + 2x)

Volume = integral of dV from 0 to 1 = (-x⁹/9 - 2x⁵/5 + x³/3 + x²) from 0 to 1

Volume = 37/45