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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 (\log x) + \cos (\log x)]} \;dx = $
  • A
    $x\cos (\log x) + c$
  • B
    $\sin (\log x) + c$
  • C
    $\cos (\log x) + c$
  • ✓
    $x\sin (\log x) + c$
✓

Answer

Correct option: D.
$x\sin (\log x) + c$
d
(d) $\int_{}^{} {\sin (\log x)\,dx} + \int_{}^{} {\cos (\log x)\,dx} $
$ = x\sin (\log x) - \int_{}^{} {\frac{{x\cos (\log x)}}{x}} \,dx + \int_{}^{} {\cos (\log x)\,dx + c} $
$ = x\sin (\log x) + c.$

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