JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x\), then \(\int_0^{21} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x\) equals :
- A \(\frac{\pi^2}{12}\)
- B \(\frac{\pi^2}{4}\)
- C \(\frac{\pi^2}{16}\)
- D \(\frac{\pi^2}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi^2}{16}\)
Step-by-step Solution
Detailed explanation
I=\int_0^{\frac{\pi}{2}} \frac{(\sin x)^{\frac{3}{2}} d x}{(\sin x)^{\frac{3}{2}} x+(\cos x)^{\frac{3}{2}}}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}}\left(\frac{\pi}{2}-x\right) d x}{\sin ^{\frac{3}{2}}\left(\frac{\pi}{2}-x\right)+\cos…
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