JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\phi(x)=\frac{1}{\sqrt{x}} \frac{\pi}{4} \int \limits_0^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, \quad x > 0\) then \(\phi^{\prime}\left(\frac{\pi}{4}\right)\) is equal to :
- A \(\frac{8}{\sqrt{\pi}}\)
- B \(\frac{4}{6+\sqrt{\pi}}\)
- C \(\frac{8}{6+\sqrt{\pi}}\)
- D \(\frac{4}{6-\sqrt{\pi}}\)
Answer & Solution
Correct Answer
(C) \(\frac{8}{6+\sqrt{\pi}}\)
Step-by-step Solution
Detailed explanation
\(\phi^{\prime}( x )=\frac{1}{\sqrt{ x }}\left[\left(4 \sqrt{2} \sin x -3 \phi^{\prime}( x )\right) \cdot 1-0\right]-\frac{1}{2} x ^{-3 / 2}\) \(\int \limits_{\frac{\pi}{4}}^{ x }\left(4 \sqrt{2} \sin t -3 \phi^{\prime}( t )\right) dt\)…
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