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OAU Post-UTME Mathematics 2019 Question 3

Question 3

Integration

Evaluate ∫cos2(90 − θ)dθ

  1. A.½[θ − (sin 2θ)/2] + K
  2. B.½θ − ½ sin 2θ + k
  3. C.½θ − ½ cos 2θ + k
  4. D.½θ − ¼ cos 2θ + k
Show the answer and explanation

Answer: A (½[θ − (sin 2θ)/2] + K)

Explanation

cos(90° − θ) = sin θ, and sin²θ = (1 − cos 2θ)/2. Integrating gives ½(θ − ½ sin 2θ) + K.