What is \int_{-1}^{1}(3 \sin x-\sin 3x)\cos^{2}x\,dx equal to ?
- A. -\frac{1}{4}
- B. 0 ✓
- C. \frac{1}{2}
- D. \frac{1}{4}
Correct Answer: B. 0
Explanation
The function h(x) = (3\sin x - \sin 3x)\cos^2 x is an odd function because \sin(-x) = -\sin x and \cos(-x) = \cos x, so h(-x) = -h(x). The integral of any odd function over a symmetric interval [-1, 1] evaluates to 0.
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