A) \[\frac{\pi }{60}\]
B) \[\frac{\pi }{20}\]
C) \[\frac{\pi }{40}\]
D) \[\frac{\pi }{80}\]
E) \[\frac{\pi }{10}\]
Correct Answer: A
Solution :
Given that, \[\int_{0}^{\infty }{\frac{{{x}^{2}}}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})({{x}^{2}}+{{c}^{2}})}}dx\] \[=\frac{\pi }{2(a+b)(b+c)(c+a)}\] On putting\[a=0,b=2,c=3\]in the above equation \[\therefore \]\[\int_{0}^{\infty }{\frac{dx}{({{x}^{2}}+4)({{x}^{2}}+9)}}\] \[=\frac{\pi }{2(2+3)(3+0)(0+2)}\] \[=\frac{\pi }{2\times 5\times 3\times 2}=\frac{\pi }{60}\]You need to login to perform this action.
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