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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

$\int \limits _0^{\omega} \large\frac{x^2}{(x^2+a^2) (x^2+b^2) (x^2+c^2)}$$dx= \large\frac{\pi}{2(a+b)(b+c)(c+a)}$ then find $\int \limits _0^{\omega} \large\frac{dx}{(x^2+4)(x^2+g)}$

\[\begin {array} {1 1} (a)\;\frac{\pi}{20} \\ (b)\;\frac{\pi}{40} \\ (c)\;\frac{\pi}{60} \\ (d)\;\frac{z}{80} \end {array}\]

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A)
Put $a=2,b=3,c=0$
=>$\int \limits _0^{\omega} \large\frac{x^2}{(x^2+4) (x^2+9) (x^2)}$$dx$
=> $\large\frac{\pi}{2(5)(3)(2)}$
=> $\large\frac{\pi}{60}$
Hence c is the correct answer.
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