Answer:
π/8
Step-by-step explanation:
∫₂°° dx / (4 + x²)
If x = 2 tan u, then dx = 2 sec²u du.
When u = π/4, x = 2. As u approaches π/2, x approaches ∞.
∫ (2 sec²u du) / (4 + 4 tan²u)
½ ∫ (sec²u du) / (1 + tan²u)
½ ∫ (sec²u du) / sec²u
½ ∫ du
½ (π/2 − π/4)
π/8
