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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
Integral of $\sqrt {1\,\, + \,\,2\,\cot \,x\,\,(\cot \,x\,\, + \,\,\cos ec\,x)} $ $w.r.t.\, x$ is :
  • A
    $2\, ln\, \cos\,\frac{x}{2}  + c$
  • ✓
    $2\, ln\, \sin\, \frac{x}{2} + c$
  • C
    $\frac{1}{2}\, ln\, cos \frac{x}{2} + c$
  • D
    $ln\,\sin\, x - ln(cosec\, x - cot\, x) + c$
✓

Answer

Correct option: B.
$2\, ln\, \sin\, \frac{x}{2} + c$
b
$I =$ $\int {\sqrt {1 + 2\cos ec\,x\;\cot x + 2{{\cot }^2}x} } $
$= \int {\sqrt {\cos e{c^2}x + 2\cos ecx\cot x + {{\cot }^2}x} \,dx} $
$= \int {(\cos ecx + \cot x)\,dx} $

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