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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
Given that $\int_0^\infty {\frac{{{x^2}\,dx}}{{({x^2} + {a^2})({x^2} + {b^2})({x^2} + {c^2})}} = \frac{\pi }{{2(a + b)(b + c)(c + a)}}} ,$ then the value of $\int_0^\infty {\frac{{{x^2}dx}}{{({x^2} + 4)({x^2} + 9)}}} $ is
  • ✓
    $\frac{\pi }{{60}}$
  • B
    $\frac{\pi }{{20}}$
  • C
    $\frac{\pi }{{40}}$
  • D
    $\frac{\pi }{{80}}$
✓

Answer

Correct option: A.
$\frac{\pi }{{60}}$
a
(a) Put $a = 2, b = 3$ and $c = 0$  in the given integral and you get the value of required integral as given in option $ (a).$

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