Evaluate ∫sec\(^2\)\theta d\theta?
A
sec θ tan θ + k
B
tan θ + k
C
2sec θ + k
D
sec θ + k
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
∫sec2\theta d\theta = ∫ 1/cos2 d\theta
∫(cos)-2 d\theta,
let u = cos \theta
∴∫u-2 = 1/u + c
∫cos \theta = sin \theta + c
∫sec-2\theta = 1/u sin \theta + c
= (sin\theta / cos\theta) + c
= Tan \theta + c
Source: Myschool Past Questions Archive (Record #9363)