Answer: π/2.
- A 2/π
- B π/2
- C π
- D 4/π
Correct answer: B. π/2
Explanation: Wallis derived this from ∫₀<sup>π/2</sup>sin<sup>2n</sup>x dx evaluated two ways. The infinite product (2/1)(2/3)(4/3)(4/5)(6/5)(6/7)... converges to π/2, giving a beautiful product representation of π.
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.