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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
$\int {x{e^{{x^2}}}} dx = $
  • A
    $ - \frac{{{e^{{x^2}}}}}{2} + c$
  • ✓
    $\frac{{{e^{{x^2}}}}}{2} + c$
  • C
    $\frac{{{e^x}}}{2} + c$
  • D
    $ - \frac{{{e^x}}}{2} + c$
✓

Answer

Correct option: B.
$\frac{{{e^{{x^2}}}}}{2} + c$
b
(b) $I = \int {x{e^{{x^2}}}dx} $$ = \frac{1}{2}\int {{e^t}dt = \frac{{{e^{{x^2}}}}}{2}} + c$.
{Put ${x^2} = t$ ==> $2xdx = dt$}

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