Question

Evaluate the integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx \]

• A. \( \frac{1 - \sin 2}{4} \)
• B. \( \frac{- (1 + \sin 2)}{4} \)
• C. \( \frac{\sin 2 - 2}{4} \)
• D. \( \frac{-(2 + \sin 2)}{4} \)

Hint:

For integrals involving trigonometric products, use appropriate identities to simplify the integrand and make the integration easier.

Answer 1

The Correct Option is D

We start by solving the given integral using standard integration techniques. After performing the necessary steps and applying the appropriate trigonometric identities, we arrive at the solution. Thus, the correct answer is option (4).