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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{{\tan }^{ - 1}}\sqrt {\frac{{1 - \cos 2x}}{{1 + \cos 2x}}} } \;dx = $
  • A
    $2{x^2} + c$
  • B
    ${x^2} + c$
  • ✓
    $\frac{{{x^2}}}{2} + c$
  • D
    $2x + c$
✓

Answer

Correct option: C.
$\frac{{{x^2}}}{2} + c$
c
(c) $\int_{}^{} {{{\tan }^{ - 1}}\sqrt {\frac{{1 - \cos 2x}}{{1 + \cos 2x}}} \,dx = \int_{}^{} {{{\tan }^{ - 1}}\tan x\,dx} } $
$ = \int_{}^{} {x\,dx = \frac{{{x^2}}}{2}} + c.$

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