Question

The integral of \( \cos^2x \) is

• A. \( \frac{1}{12} \sin 3x + \frac{3}{4} \sin x + c \)
• B. \( \frac{1}{12} \sin 3x + \frac{1}{4} \sin x + c \)
• C. \( \frac{1}{12} \sin 3x - \frac{3}{4} \sin x + c \)
• D. \( \frac{1}{12} \sin 3x - \frac{1}{4} \sin x + c \)

Hint:

When dealing with trigonometric integrals, use identities to simplify the integrand before integrating.

Answer 1

The Correct Option is B

Step 1: Use a trigonometric identity.
We use the identity \( \cos^2x = \frac{1 + \cos 2x}{2} \) to rewrite the integrand. Step 2: Integrate the expression.
After integrating, the result is \( \frac{1}{12} \sin 3x + \frac{1}{4} \sin x + c \). Step 3: Conclusion.
Thus, the correct answer is (B).