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Today's Calculation of Integral 50

Source: 2004 Tokyo University of Science

June 20, 2005
calculusintegrationlimitlogarithmsalgebrapolynomialderivative

Problem Statement

Let a,ba,b be real numbers such that a<ba<b. Evaluate lim⁡b→a∫abln⁡∣1+(x−a)(b−x)∣dx(b−a)3\lim_{b\rightarrow a} \frac{\displaystyle\int_a^b \ln |1+(x-a)(b-x)|dx}{(b-a)^3}.
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