REduction definite Integral

IIT JEE Papers › Calculus questions › REduction definite Integral

\dpi{120} \hspace{-16}$If $\mathbf{I_{1}=\int_{0}^{\infty}(1+x^2)^{-2012}dx}$ and $\mathbf{I_{2}=\int_{0}^{\infty}(1+x^2)^{-2011}dx}$\\\\\\ Then find value of $\mathbf{\frac{I_{1}}{I_{2}}=}$

Ans=(4021)/(4022)

#Mathematics #Calculus

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Aditya Bhutra ·2012-02-21 09:36:00

use integration by parts for I₂

then a slight manipulation in the second term .

Quite easy after that.

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Vivek @ Born this Way ·2012-02-21 10:14:10

Very similar to what asked in one of previous IIT's if I remember correctly.

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REduction definite Integral

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