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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate $\int \limits_0^3 \sqrt {\large\frac{x}{3-x}}$$dx$

\[\begin {array} {1 1} (a)\;\frac{5x}{2} \\ (b)\;\frac{3z}{2} \\ (c)\;2z\\ (d)\;3z \end {array}\]

Can you answer this question?
 
 

1 Answer

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$x= 3 \sin ^2 \theta,$ at $x=0, limit=0$
$dx= 6 \sin \theta \cos \theta, x=3, limit=\large\frac{z}{2}$
=> $\int \limits_0^{\large\frac{z}{2}} \tan \theta. 6. \sin \theta . \cos \theta$
=> $\int \limits_0^{\large\frac{z}{2}} 6 \sin ^2 \theta . d\theta$
=> $3 \int _0^{\large\frac{z}{2}}1- \cos 2 \theta d\theta$
=> $ 3[ \theta ]_0^{z/2}-3 [\sin ]_0^{z/2}$
=> $ 3[ \large\frac{z}{2}$$-0]-3[\sin z- \sin 0]$
=> $ \large\frac{3z}{2}$
answered Dec 12, 2013 by meena.p
 
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