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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
The value of $\int_{}^{} {\frac{{\sin x}}{{{{\cos }^2}x}}\;dx} $ is
  • A
    $\sin x + k$
  • B
    $\tan x + k$
  • ✓
    $\sec x + k$
  • D
    $\tan x + \sec x + k$
✓

Answer

Correct option: C.
$\sec x + k$
c
(c) Given $I = \int_{}^{} {\frac{{\sin x}}{{{{\cos }^2}x}}} \,dx$.

Put $\cos x = t \Rightarrow \sin x\,dx = - dt$
$\therefore \,\,\,I = \int_{}^{} {\frac{{ - dt}}{{{t^2}}}} = \frac{1}{t} + k = \sec x + k$.

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