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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_{\pi / 6}^{\pi / 4} \operatorname{cosec} 2 x d x=$
  • A
    $\log 3$
  • B
    $\log \sqrt{3}$
  • C
    $\log 9$
  • ✓
    $\frac{1}{2} \log \sqrt{3}$
✓

Answer

Correct option: D.
$\frac{1}{2} \log \sqrt{3}$
(D)
$\int_{\pi / 6}^{\pi / 4} \operatorname{cosec} 2 x d x=\frac{1}{2}[\log \tan x]_{\frac{\pi}{6}}^{\frac{\pi}{4}}$
$=\frac{1}{2}\left[\log \tan \frac{\pi}{4}-\log \tan \frac{\pi}{6}\right]$
$=\frac{1}{2} \log \sqrt{3}$

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