If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), ... VIDEO
If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), then \( \int_{\alpha}^{\beta} f(x) g^{\prime}(x) d x \) is equal
(a) \( \int_{\alpha}^{\beta} f^{\prime}(x) g(x) d x \)
(b) \( -\int_{\alpha}^{\beta} f^{\prime}(x) g(x) d x \)
(c) \( \frac{1}{2} \int_{\alpha}^{\beta}\left(f(x) g^{\prime}(x)-f^{\prime}(x) g(x)\right) d x \)
(d) \( \frac{1}{2} \int_{\alpha}^{\beta}\left(f(x) g^{\prime}(x)+f^{\prime}(x) g(x)\right) d x \)
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