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JEE Main 06-Apr-2024 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 06-Apr-2024 Paper - Shift 14 Marks
MCQ
$\int_0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x$ is equal to
  • A
    $1 / 12$
  • B
    $1 / 9$
  • C
    $\text { 1/6 }$
  • D
    $1 / 3$
✓

Answer

Divide Nr\&Dr by cosx
$\int_0^{\pi / 4} \frac{\tan ^2 x \sec ^2 x d x}{\left(1+\tan ^3 x\right)^2} d x$
Let $1+\tan ^3 x = t$
$\tan ^2 x \sec ^2 x d x=\frac{d t}{3}$
$\frac{1}{3} \int_1^2 \frac{dt}{t^2}=\frac{1}{6}$

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