The double integral from 0 to π/2 and 0 to π/2 of sin(x + y) dx dy is
- A. 0
- B. π
- C. π/2
- D. 2
Answer: D. 2
Explanation: ∫₀^(π/2) ∫₀^(π/2) sin(x + y) dx dy = ∫₀^(π/2) [−cos(x + y)]₀^(π/2) dy = ∫₀^(π/2) [cos y + sin y] dy = [sin y − cos y]₀^(π/2) = (1 − 0) − (0 − 1) = 2.