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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
$\int_{}^{} {({{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x)\;dx = } $
  • A
    $\frac{1}{2}\pi x + c$
  • B
    $x({\cos ^{ - 1}}x + {\sin ^{ - 1}}x) + c$
  • ✓
    Both $ (a)$ and $(b)$
  • D
    $\frac{\pi }{2} + x + c$
✓

Answer

Correct option: C.
Both $ (a)$ and $(b)$
c
(c) $\int_{}^{} {({{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x)\,dx} = \int_{}^{} {\left( {\frac{\pi }{2}} \right)} \,dx = \frac{{\pi x}}{2} + c$
$\left( \because \,\,\,{{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} \right)$
Also $\int_{}^{} {({{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x)dx = x({{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x) + c} $.

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