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STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
$\int\limits_{\pi /2}^\pi  {\,\frac{{1 - \sin x}}{{1 - \cos x}}} $ $dx =$
  • ✓
    $1 - ln 2$
  • B
    $ln 2$
  • C
    $1 + ln 2$
  • D
    $none$
✓

Answer

Correct option: A.
$1 - ln 2$
a
$I\,\, = \,\int {\frac{{1 - \sin x}}{{2{{\sin }^2}\frac{x}{2}}}\,\,\,\,dx} $= $\int {\left( {\frac{1}{2}\,\cos e{c^2}\frac{x}{2} - \cot \frac{x}{2}} \right)\,dx} $ $= -x cot$$\left. {\frac{x}{2}} \right|_{\,\frac{\pi }{2}}^{\,\pi }$

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