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Today's calculation of Integral 818

Source: 2012 Tokyo Medical and Dental University entrance exam

May 16, 2012
calculusintegrationfunctionlimitlogarithmsLaTeXabsolute value

Problem Statement

For a function f(x)=x3−x2+xf(x)=x^3-x^2+x, find the limit lim⁡n→∞∫n2n1f−1(x)3+∣f−1(x)∣ dx.\lim_{n\to\infty} \int_{n}^{2n}\frac{1}{f^{-1}(x)^3+|f^{-1}(x)|}\ dx.
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