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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
If $\beta + 2 \int\limits_0^1 {{x^2}\,\,{e^{ - {x^2}}}}$ $dx = \int\limits_0^1 {{e^{ - {x^2}}}}\, dx$ then the value of $\beta$ is
  • ✓
    $e^{-1}$
  • B
    $e$
  • C
    $1/2e$
  • D
    can not be determined
✓

Answer

Correct option: A.
$e^{-1}$
a
$\beta + \int\limits_0^1 \,  x. 2 x {e^{ - \,{x^2}}}$  $d x = \int\limits_0^1 \, {e^{ - \,{x^2}}} d x$
$\beta + \left[ {\, - \,x\,{e^{ - \,{x^2}}}\,} \right]_0^1 - \int\limits_0^1 \, -  {e^{ - \,{x^2}}}\, d x\, = d x\, $

$\beta = \frac{1}{e}$

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