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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
The value of $\int_0^{\frac{\pi}{2}} \frac{ e ^{x^2}}{ e ^{x^2}+ e ^{\left(\frac{\pi}{2}-x\right)^2}} d x$ is
  • ✓
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • C
    $e^{\frac{\pi^2}{16}}$
  • D
    $e^{\frac{\pi^2}{4}}$
✓

Answer

Correct option: A.
$\frac{\pi}{4}$
(A)
Here, $f (x)= e ^{x^2}$ and $a =\frac{\pi}{2}$
$\int_0^{ a } \frac{ f (x)}{ f (x)+ f ( a -x)} d x=\frac{ a }{2}$
$\int_0^{\frac{\pi}{2}} \frac{ e ^{x^2}}{ e ^{x^2}+ e ^{\left(\frac{\pi}{2}-x\right)^2}} d x=\frac{\frac{\pi}{2}}{2}=\frac{\pi}{4}$

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