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7.1 inderfinite integral — Maths STD 12 Science — Question

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

Answer

Correct option: D.
${\sin ^{ - 1}}x + \sqrt {1 - {x^2}} + c$
d
(d)$\int_{}^{} {\sqrt {\frac{{1 - x}}{{1 + x}}} \,dx} = \int_{}^{} {\frac{{1 - x}}{{\sqrt {1 - {x^2}} }}} \,dx = \int_{}^{} {\frac{1}{{\sqrt {1 - {x^2}} }}} \,dx - \int_{}^{} {\frac{{x\,dx}}{{\sqrt {1 - {x^2}} }}} $
Now proceed yourself.

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