Let \( f(x) \) be a continuous function and \( I=\int_{1}^{9} \sqrt... VIDEO
Let \( f(x) \) be a continuous function and \( I=\int_{1}^{9} \sqrt{x} f(x) d x \), then
(A) There exists some \( c \in(1,9) \) such that \( I=8 \sqrt{c} f(c) \)
(B) There exists some \( p, q \in(1,3) \) such that \( I=2\left[p^{2} f\left(p^{2}\right)+q^{2} f\left(q^{2}\right)\right] \)
(C) There exists some \( \alpha \in(1,9) \) such that \( I=9 \sqrt{\alpha} f(\alpha) \)
(D) If \( f(x) \geq 0 \forall x \in[1,9] \Rightarrow I0 \)
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