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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^{{{\cos }^2}x}}\sin 2x\;dx = } $
  • A
    ${e^{{{\cos }^2}x}} + c$
  • ✓
    $ - {e^{{{\cos }^2}x}} + c$
  • C
    $1/2{e^{{{\cos }^2}x}} + c$
  • D
    None of these
✓

Answer

Correct option: B.
$ - {e^{{{\cos }^2}x}} + c$
b
(b) Put $t = {\cos ^2}x \Rightarrow dt = - \sin 2x\,dx,$ then
$\int_{}^{} {{e^{{{\cos }^2}x}}\sin 2x\,dx} = - \int_{}^{} {{e^t}dt} = - {e^t} + c = - {e^{{{\cos }^2}x}} + c.$

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