Question

The correct evaluation of \[ \int_0^{\frac{\pi}{2}} \sin^4 x \, dx \] is:

• A. \( \frac{8\pi}{3} \)
• B. \( \frac{2\pi}{3} \)
• C. \( \frac{4\pi}{3} \)
• D. \( \frac{3\pi}{8} \)

Hint:

Use reduction formulas or trigonometric identities to simplify higher powers of trigonometric functions before integrating.

Answer 1

The Correct Option is B

Step 1: Use the reduction formula or trigonometric identity to simplify \( \sin^4 x \).
Step 2: After simplification and integration, we obtain \( \frac{2\pi}{3} \).

Final Answer: \[ \boxed{\frac{2\pi}{3}} \]