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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate :$\int \limits_3^4 \large\frac{1}{\sqrt {(x-3)(4-x)}} $$dx$

\[\begin {array} {1 1} (a)\;\pi \\ (b)\;\frac{\pi}{2} \\ (c)\;2\pi\\ (d)\;(\pi)^2 \end {array}\]

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1 Answer

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Given $\int \limits_3^4 \large\frac{1}{\sqrt {(x-3)(4-x)}} $$dx$
$\int \limits_{\alpha}^{\beta} \large\frac{1}{\sqrt {(x-\beta)(\beta-x)}} $$dx=\pi, \beta > \alpha$
$\alpha=3$
$\beta=4$
$\beta > \alpha$
using this value we get $\pi$
answered Dec 12, 2013 by meena.p
edited Mar 20, 2014 by balaji.thirumalai
 
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