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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Evaluate the following integral: $\int\sec^2\text{xdx:}$
  • A
    $2\tan\text{x+c}$
  • B
    $\tan2\text{x}+\text{c}$
  • ✓
    $\tan\text{x}+\text{c}$
  • D
    None of these
✓

Answer

Correct option: C.
$\tan\text{x}+\text{c}$
We know that. $\frac{\text{d}}{\text{dx}}(\tan\text{x})=\sec^2\text{x}$
$\therefore\text{d }(\tan\text{x})=\sec^2\text{xdx}$
$\Rightarrow\text{I}=\int\sec^2\text{xdx}=\tan\text{x+c}$

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