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Today's calculation of Integral 114

Source: Shibaura Institute of Technology entrance exam 2006

July 7, 2006
calculusintegrationcalculus computations

Problem Statement

Let aa be positive numbers.For xa,|x|\leq a, find the maximum and minimum value of xax+a4a2t2 dt.\int_{x-a}^{x+a}\sqrt{4a^{2}-t^{2}}\ dt.