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Mathematics

Hot goIITian

 Joined: 15 Feb 2012 Post: 180
4 May 2012 10:22:00 IST
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Engineering Entrance , JEE Main , CBSE Board , JEE Main & Advanced , Mathematics , Integral Calculus , CBSE XII (Science) , Mathematics I , Mathematics II

Hint : use substitution

Blazing goIITian

Joined: 19 Jan 2008
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4 May 2012 22:54:01 IST
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$\hspace{-16}First we will Chech that the Given Integral is Convergent\\\\\\ \bf{\mathbb{O}}r Divergent in \bf{x\in \left( 0,\frac{3}{2}\right )}\\\\\\ for that \bf{x\sqrt{81-9x^2}+x^2-9=0}, Where \bf{x\leq 3}\\\\\\ \bf{x^2.(81-9x^2)=(9-x^2)^2}\\\\\\ \bf{9x^2.(9-x^2)-(9-x^2)^2=0}\\\\\\ \bf{(9-x^2).(9x^2-9+x^2)=0}\\\\\\ So \bf{x=\pm 3} and \bf{x=\frac{3}{\sqrt{10}}\in \left(0,\frac{3}{2}\right)}\\\\\\ So The Given Integrant is Not Defined at \bf{x=\frac{3}{\sqrt{10}}}\\\\\\ So It Shows a Logarithmic Divergence of Integral..........$

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