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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_0^{\pi \,/\,2n} {\,\frac{{dx}}{{1\,\, + \,\,{{\tan }^n}\,nx}}} $ =
  • A
    $0$
  • ✓
    $\frac{\pi }{{4\,n}}$
  • C
    $\frac{{n\,\pi }}{4}$
  • D
    $\frac{\pi }{{2\,n}}$
✓

Answer

Correct option: B.
$\frac{\pi }{{4\,n}}$
b
$nx = t;I = $ $\frac{1}{n}\int\limits_0^{\frac{\pi }{2}} {\frac{{dt}}{{1 + {{(\tan t)}^n}}}} $ =  $\frac{1}{n}\int\limits_0^{\frac{\pi }{2}} {\frac{{{{(\cos t)}^n}}}{{{{(\sin t)}^n} + {{(\cos t)}^n}}}\,dt} $

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