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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
If $\int\sin\text{xd}(\sec\text{x})=\text{f}(\text{x})-\text{g}(\text{x})+\text{c},$ then :
  • A
    $\text{f}(\text{x})=\sec\text{x}$
  • ✓
    $\text{f}(\text{x})=\tan\text{x}$
  • C
    $\text{g}(\text{x})=2\text{x}$
  • D
    $\text{g}=-\text{x}$
✓

Answer

Correct option: B.
$\text{f}(\text{x})=\tan\text{x}$
$\int\sin \text{xd}(\sec\text{x})=\int\sin\text{x}\sec\text{x}\tan\text{x dx}$
$=\int\tan^2\text{x dx}$
$=\int(\sec^2\text{x - 1})\text{dx}$
$=\tan\text{x - x}+\text{c}$
$\Rightarrow\text{f}(\text{x})=\tan\text{x},\text{g}(\text{x})=\text{x}$

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