If \( f(x)=\int_{0}^{\pi} \frac{t \sin t d t}{\sqrt{1+\tan ^{2} x \... VIDEO
If \( f(x)=\int_{0}^{\pi} \frac{t \sin t d t}{\sqrt{1+\tan ^{2} x \sin ^{2} t}} \) for \( 0x\frac{\pi}{2} \), then
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(1) \( f\left(0^{+}\right)=-\pi \)
(2) \( f\left(\frac{\pi}{4}\right)=\frac{\pi^{2}}{8} \)
(3) \( f \) is continuous and differentiable in \( \left(0, \frac{\pi}{2}\right) \)
(4) \( f \) is continuous but not differentiable in \( \left(0, \frac{\pi}{2}\right) \)
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