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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
If $\int_{}^{} {\frac{{f(x)\;dx}}{{\log \sin x}} = \log \log \sin x} $, then $f(x) = $
  • A
    $\sin x$
  • B
    $\cos x$
  • C
    $\log \sin x$
  • ✓
    $\cot x$
✓

Answer

Correct option: D.
$\cot x$
d
(d)$\int_{}^{} {\frac{{f(x)\,dx}}{{\log \sin x}}} = \log \log \sin x$
Differentiating both sides, we get
$\frac{{f(x)}}{{\log \sin x}} = \frac{{\cot x}}{{\log \sin x}} \Rightarrow f(x) = \cot x.$

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