Evaluate ∫sec2θ dθ
-
A.
sec θ tan θ + k -
B.
tan θ + k -
C.
2sec θ + k -
D.
sec θ + k
Correct Answer: Option B
Explanation
∫sec2θ dθ = ∫ 1/cos2 dθ
∫(cos)-2 dθ,
let u = cos θ
∴∫u-2 = 1/u + c
∫cos θ = sin θ + c
∫sec-2θ = 1/u sin θ + c
= (sinθ / cosθ) + c
= Tan θ + c