A) \[\frac{\pi }{20}\]
B) \[\frac{\pi }{40}\]
C) \[\frac{\pi }{60}\]
D) \[\frac{\pi }{80}\]
Correct Answer: C
Solution :
Given, \[\int_{0}^{\infty }{\frac{{{x}^{2}}dx}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})({{x}^{2}}+{{c}^{2}})}}\] \[=\frac{\pi }{2(a+b)(b+c)(c+a)}\] Put\[a=2,\text{ b}=3\]and\[c=0\] \[\int_{0}^{\infty }{\frac{{{x}^{2}}dx}{({{x}^{2}}+4)({{x}^{2}}+9)}=\frac{\pi }{2(2+3)(3+0)(0+2)}}\] \[=\frac{\pi }{2.5.3.2}=\frac{\pi }{60}\]You need to login to perform this action.
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