Question:
Evaluate the integral:
\[
\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx
\]
Evaluate the integral:
\[
\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx
\]
Show Hint
For integrals involving trigonometric products, use appropriate identities to simplify the integrand and make the integration easier.
Updated On: May 15, 2025
- \( \frac{1 - \sin 2}{4} \)
- \( \frac{- (1 + \sin 2)}{4} \)
- \( \frac{\sin 2 - 2}{4} \)
- \( \frac{-(2 + \sin 2)}{4} \)
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The Correct Option is D
Solution and Explanation
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).
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