Answer: π/2.
- A π/2
- B π/3
- C π/4
- D π/6
Correct answer: A. π/2
Explanation: Shell method: V = 2π∫₀¹ x·f(x)dx = 2π∫₀¹ x·x² dx = 2π∫₀¹ x³ dx = 2π[x⁴/4]₀¹ = 2π·(1/4) = π/2 cubic units.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.