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12th Class Mathematics Definite Integrals Question Bank Critical Thinking

  • question_answer
    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 [Karnataka CET 1993]

    A) \[\frac{\pi }{60}\]               

    B) \[\frac{\pi }{20}\]

    C) \[\frac{\pi }{40}\]               

    D) \[\frac{\pi }{80}\]

    Correct Answer: A

    Solution :

    Put \[a=2,\]\[b=3\]and \[c=0\]in the given integral and you get the value of required integral as given in option.


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