Let u = _0^ , , dx x^4 , , + , ,7 x^2 , , + , ,1 & v = _0^ , , x^… - Vidyadip

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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