Answer: π/4.
- A 0
- B π/4
- C π/2
- D 1
Correct answer: B. π/4
Explanation: King's rule: let I = ∫₀<sup>π/2</sup> sinⁿx/(sinⁿx+cosⁿx)dx. Replace x→(π/2−x): get ∫cosⁿx/(cosⁿx+sinⁿx)dx. Adding both: 2I = ∫₀<sup>π/2</sup>1 dx = π/2. So I = π/4.
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.