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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: evaluate this integral..
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[Post New]23 Mar 2008 11:44:15 IST
    Subject: evaluate this integral..
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kasirajan.1990 (1084)

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   evaluate :           \int_0^{1/4} \frac {dx} {1 + (cot{2{\pi}x})^{1/2} } 
kasirajan



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[Post New]23 Mar 2008 11:54:27 IST
    Subject: Re:evaluate this integral..
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raulrag009 (1217)

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Here\\\\ I=\int_{0}^{\frac{1}{4}}{\frac{dx}{1+\sqrt{\cot{2\pi\;x}}}}\\\\ I=\int_{0}^{\frac{1}{4}}{\frac{\sqrt{\tan{2\pi\;x}}}{1+\sqrt{\tan{2\pi\;x}}}}..............(1)\\\\ Apply\;property\\\\ I=\int_{0}^{\frac{1}{4}}{\frac{dx}{1+\sqrt{\tan{2\pi\;x}}}}.............(2)\\\\ Add\;(1)\;and\;(2)\\\\ 2I=\int_{0}^{\frac{1}{4}}{\frac{\sqrt{\tan{2\pi\;x}}}{1+\sqrt{\tan{2\pi\;x}}}}+\int_{0}^{\frac{1}{4}}{\frac{dx}{1+\sqrt{\tan{2\pi\;x}}}}\\\\ 2I=\int_{0}^{\frac{1}{4}}{dx}\\\\ 2I=\frac{1}{4}\\\\ I=\frac{1}{8}
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