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Integral Calculus

Blazing goIITian

Joined:	12 Apr 2008
Post:	2717

8 Jul 2009 21:12:51 IST

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408

Need help :)

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

then equals,

$(a)\ 2\pi$

$(b)\ \pi$

$(c)\ \frac\pi{2}$

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

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Comments (3)

akki ~~ unlucky forever ~~

Blazing goIITian

Joined: 11 May 2008

Posts: 491

8 Jul 2009 21:32:45 IST

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$put\ x=sin^2\theta \\ \\ \\ \\ I=2\int_{0}^{\frac{\pi}{2}}(\frac{1}{(1+sin^2\theta)}-\frac{1}{(2+sin^2\theta)})d\theta \\ \\ \\ \\ I = \frac{\pi(\sqrt{3}-1)}{\sqrt6}$

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

Posts: 5517

8 Jul 2009 21:41:28 IST

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Great !!

taran

Blazing goIITian

Joined: 17 Nov 2008

Posts: 1331

8 Jul 2009 21:42:28 IST

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cheers

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