_ ^ x ;dx =

MCQ

$\int_{}^{} {\sin \sqrt x } \;dx = $

A
$2[\sin \sqrt x - \cos \sqrt x ] + c$
✓
$2[\sin \sqrt x - \sqrt x \cos \sqrt x ] + c$
C
$2[\sin \sqrt x + \cos \sqrt x ] + c$
D
$2[\sin \sqrt x + \sqrt x \cos \sqrt x ] + c$

✓

Answer

Correct option: B.

$2[\sin \sqrt x - \sqrt x \cos \sqrt x ] + c$

b
(b) Put $\sqrt x = t \Rightarrow \frac{1}{{2\sqrt x }}\,dx = dt \Rightarrow dx = 2t\,dt,$ then
$\int_{}^{} {\sin \sqrt x \,dx} = 2\int_{}^{} {t\sin t\,dt} = 2( - t\cos t + \sin t) + c$
$ = 2(\sin \sqrt x - \sqrt x \cos \sqrt x ) + c.$

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