_ ^ ( ^ - 1 x + ^ - 1 x) ;dx = - Vidyadip

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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