JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int_0^{\frac{\pi}{4}} \frac{x d x}{\sin ^4(2 x)+\cos ^4(2 x)}\) equals :
- A \(\frac{\sqrt{2} \pi^2}{8}\)
- B \(\frac{\sqrt{2} \pi^2}{16}\)
- C \(\frac{\sqrt{2} \pi^2}{32}\)
- D \(\frac{\sqrt{2} \pi^2}{64}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{2} \pi^2}{32}\)
Step-by-step Solution
Detailed explanation
\(\int_0^{\frac{\pi}{4}} \frac{x d x}{\sin ^4(2 x)+\cos ^4(2 x)}\) Let \(2 x=t\) then \(d x=\frac{1}{2} d t\) \(I=\frac{1}{4} \int_0^{\frac{\pi}{2}} \frac{t d t}{\sin ^4 t+\cos ^4 t}\)…
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