Step-by-step explanation:
π ∫₀¹ x² dx
This integral is obtained using disk method. Each disk has a volume of V = πr²t, so the radius is r = x.
The region is 0 ≤ y ≤ x, 0 ≤ x ≤ 1.
Revolved around the x-axis, the resulting shape is a cone.
If the shape were a paraboloid, the integral would have been:
π ∫₀¹ (x²)² dx
π ∫₀¹ x⁴ dx
