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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
Let $I_1 = \int\limits_0^{\frac{\pi }{2}} {{e^{ - {x^2}}}\sin (x)dx} $ ; $I_2 = \int\limits_0^{\frac{\pi }{2}} {{e^{ - {x^2}}}dx} $ ; $I_3 = \int\limits_0^{\frac{\pi }{2}} {{e^{ - {x^2}}}(1 + x)\,dx} $

and consider the statements

$I\,:$ $I_1 < I_2$   

$II\,:$  $I_2 < I_3$ 

$III\,:$  $I_1 = I_3$

Which of the following is $(are)$ true?

  • A
    $I$ only
  • B
    $II$ only
  • C
    Neither $I$ nor $II$ nor $III$
  • ✓
    Both $I$ and $II$
✓

Answer

Correct option: D.
Both $I$ and $II$
d
since $0 < \sin \,x < 1$ and $1 + x > 1$ in $(0, \pi /2)$
hence $I_3 > I_2 > I_1$.
$\Rightarrow \,A$ and $B$ 

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