JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\int_0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x\) is equal to
- A \(1 / 12\)
- B \(1 / 9\)
- C \(1 / 6\)
- D \(1 / 3\)
Answer & Solution
Correct Answer
(C) \(1 / 6\)
Step-by-step Solution
Detailed explanation
Divide \(\mathrm{Nr}\ \&\ \mathrm{Dr}\) by \(\cos \mathrm{x}\) \(\int_0^{\pi / 4} \frac{\tan ^2 x \sec ^2 x d x}{\left(1+\tan ^3 x\right)^2} d x\) Let \(1+\tan ^3 \mathrm{x}=\mathrm{t}\) \(\tan ^2 \mathrm{x} \sec ^2 \mathrm{x} d \mathrm{x}=\frac{\mathrm{dt}}{3}\)…
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