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[Post New] 8 Jul 2009 21:12:51 IST
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®µD®A (2710)

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If

I=\int_0^{1}\frac{dx}{(1+x)(2+x)\sqrt{x(1-x)}}

then I equals,

(a)\ 2\pi

 

(b)\ \pi

 

(c)\ \frac\pi{2}

 

(d)\ \frac{\pi}{\sqrt6}(\sqrt3-1)


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[Post New] 8 Jul 2009 21:32:45 IST
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akki ~~ unlucky forever ~~ (1635)

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put\ x=sin^2\theta \\ \\ \\ \\ I=2\int_{0}^{\frac{\pi}{2}}(\frac{1}{(1+sin^2\theta)}-\frac{1}{(2+sin^2\theta)})d\theta \\ \\ \\ \\ I = \frac{\pi(\sqrt{3}-1)}{\sqrt6}
all's well that end's well, but if it dosen't, then it is not the end . . .
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[Post New] 8 Jul 2009 21:41:28 IST
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NugoRama (4800)

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Great !!
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[Post New] 8 Jul 2009 21:42:28 IST
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taran (1635)

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cheers
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