Question

Evaluate the following:

Options are:
pi/2
pi/8
pi
Does not converge

Answer 1

π/8

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