Find the volume of in the solid obtained by rotating the region in the first quadrant bounded by y=x^6, y=1, and the y-axis around the x-axis.

Answer 1

x⁶ = 1; x = 1; v = π∫₀¹(1 - x¹²)dx = π(x - x¹³/13)₀¹ = 12π/13