Question

The value of \[ \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^4 \theta \, d\theta \] is

• A. \( \frac{16}{1155} \)
• B. \( \frac{16}{115} \)
• C. \( \frac{385}{1155} \)
• D. \( \frac{385}{16\pi} \)

Hint:

For integrals involving powers of trigonometric functions, use reduction formulas or standard integral tables for simplification.

Answer 1

The Correct Option is A

The integral is evaluated using standard trigonometric integral techniques, leading to the result \( \frac{16}{1155} \).