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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
$\int\frac{\cos2\text{x}-1}{\cos2\text{x}+1}\text{ dx}=$
  • A
    $\tan\text{x}-\text{x}+\text{C}$
  • B
    $\text{x}+\tan\text{x}+\text{C}$
  • ✓
    $\text{x}-\tan\text{x}+\text{C}$
  • D
    $-\text{x}-\cot\text{x}+\text{C}$
✓

Answer

Correct option: C.
$\text{x}-\tan\text{x}+\text{C}$
$\text{I}=\int\frac{\cos2\text{x}-1}{\cos2\text{x}+1}\text{ dx}$
$\text{I}=-\int\frac{1-\cos2\text{x}}{1+\cos2\text{x}}\text{ dx}$

$\text{I}=-\int\frac{2\sin^2\text{x}}{2\cos^2\frac{\text{x}}{2}}\text{ dx}$

$\text{I}=-\int\tan^2\text{x dx}$

$\text{I}=-\int(\sec^2\text{x}-1)\text{dx}$

$\text{I}=-(\tan\text{x}-\text{x})+\text{C}$

$\text{I}=\text{x}-\tan\text{x}+\text{C}$

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