Question Detail

To evaluate ∫₀^(π/2) cos² x dx, use the trigonometric identity cos² x = (1 + cos 2x)/2. Substitute this into the integral: ∫₀^(π/2) (1 + cos 2x)/2 dx = (1/2) ∫₀^(π/2) (1 + cos 2x) dx. Integrate term by term: (1/2) [x + (sin 2x)/2] from 0 to π/2. Now, evaluate the definite integral by plugging in the limits: (1/2) [(π/2 + (sin(2π/2))/2) - (0 + (sin(20))/2)] = (1/2) [(π/2 + sin π/2) - (0 + sin 0/2)] = (1/2) [(π/2 + 0) - (0 + 0)] = (1/2) (π/2) = π/4.