Evaluate $\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta$

Analyze the question: We need the definite integral of sec²θ from 0 to π/4.

Concept: The derivative of tan θ is sec²θ, so the integral of sec²θ dθ is tan θ + C.

Solution:

We know tan(π/4) = tan 45° = 1 and tan 0 = 0, so:

Answer: The value is 1, which is option A.

Tip: Memorise the pairs of trig derivatives and integrals: d/dθ(tan θ) = sec²θ, so ∫sec²θ dθ = tan θ. Also remember the key values: tan 0 = 0, tan 45° = 1. In JAMB, be careful that π/4 is in radians (equal to 45°), so your calculator should be in radian mode if you use it, though here you do not need one.