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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{e^x}\sin ({e^x})} \;dx = $
  • ✓
    $ - \cos {e^x} + c$
  • B
    $\cos {e^x} + c$
  • C
    $ - {\rm{cosec}}\,{e^x} + c$
  • D
    None of these
✓

Answer

Correct option: A.
$ - \cos {e^x} + c$
a
(a)$\int_{}^{} {{e^x}\sin ({e^x})\,dx} $
Put ${e^x} = t$ and ${e^x}dx = dt,$ the integral reduces to
$\int_{}^{} {\sin t\,dt} = - \cos t + c = - \cos ({e^x}) + c.$

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