If $\phi(x)=\frac{1}{\sqrt{x}} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x0$, then $\phi^{\prime}\left(\frac{\pi}{4}\right)$ is equal to: [JEE Main 2023, 31 Jan (Shift 2)]

Question

If $\phi(x)=\frac{1}{\sqrt{x}} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0$, then $\phi^{\prime}\left(\frac{\pi}{4}\right)$ is equal to: [JEE Main 2023, 31 Jan (Shift 2)]

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If \(\phi(x)=\frac{1}{\sqrt{x}} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0\), t…

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If \(\phi(x)=\frac{1}{\sqrt{x}} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x&gt;0\), t…

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If \(\phi(x)=\frac{1}{\sqrt{x}} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0\), t…