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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $ \int \sqrt {2x^2-5x +6 } $$dx$

$(a)\;\sqrt {2} \bigg\{ \frac{1}{2} (x- \frac{5}{4} \times \sqrt {(\frac{\sqrt {23}}{4})^2 +(x-\frac{5}{4})^2 }+\large\frac{1}{2} (\frac{\sqrt {23}}{4})^2 \log \{(x -\frac{5}{4})+ \sqrt {x^2-\frac{5x}{2}+\frac{6}{2}}\} \bigg\}+c \qquad (b)\;\tan ^{-1} 3x. \log (\tan ^{-1} 3x)+c \qquad (c)\;\frac{1}{12} \{\tan ^{-1} 3x. \log (\tan ^{-1} 3x)-\tan ^{-1} 3x\} \qquad (d)\;None$

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1 Answer

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$\sqrt {2} \int \sqrt {x^2 -\large\frac{5}{2} x+3}$$dx$
=> $\sqrt {2} \int \sqrt {(x-\large\frac{5}{4})^2 + (\large\frac{\sqrt {23}}{4})^2}$
$\sqrt {2} \bigg\{ \frac{1}{2} (x- \frac{5}{4} \times \sqrt {(\frac{\sqrt {23}}{4})^2 +(x-\frac{5}{4})^2 }+\large\frac{1}{2} (\frac{\sqrt {23}}{4})^2 \log \{(x -\frac{5}{4})+ \sqrt {x^2-\frac{5x}{2}+\frac{6}{2}}\} \bigg\}+c$
Hence a is the correct answer.
answered Dec 23, 2013 by meena.p
 
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