A volume; disk method question

Question

Find the volume of the slid whose base is the region in the first quadrant bounded by y=x^7, y=1 and the y-axis and whose cross-sections perpendicular to the x axis are squares.

Volume=?

Answer 1

Volume V = ∫₀¹(1 - x⁷)²dx = ∫₀¹(1 - 2x⁷ + x¹⁴)dx = (x - x⁸/4 + x¹⁵/15)₀¹ = 1 - 1/4 + 1/15 = 49/60