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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
Let $u =$ $\int\limits_0^\infty  {\,\,\frac{{dx}}{{{x^4}\,\, + \,\,7{x^2}\,\, + \,\,1}}} $ & $v =$ $\int\limits_0^\infty  {\,\,\frac{{{x^2}\,\,\,\,dx}}{{{x^4}\,\, + \,\,7{x^2}\,\, + \,\,1}}} $ then :
  • A
    $v > u$
  • B
    $6 v = \pi$
  • C
    $3u + 2v = 5\pi /6$
  • ✓
    All of the above
✓

Answer

Correct option: D.
All of the above
d
put $x = 1/t$ in $u$ or $v \Rightarrow u = v$. Now consider $u + v$

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