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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
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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