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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}(1 - \cot x + {{\cot }^2}x)\,\,dx} $ equals
  • A
    ${e^x}\cot x + c$
  • B
    ${e^x}{\rm{cosec }}x + c$
  • ✓
    $ - {e^x}\cot x + c$
  • D
    $ - {e^x}{\rm{cosec}}\,x + c$
✓

Answer

Correct option: C.
$ - {e^x}\cot x + c$
c
(c) $I = \int {{e^x}(1 - \cot x + {{\cot }^2}x)\,dx} = \int {{e^x}( - \cot x + {\rm{cose}}{{\rm{c}}^2}x)\,dx} $
$ = {e^x}( - \cot x) + c$$ = - {e^x}\,\cot x + c$.

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