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Today's calculation of Integral 135

Source: Tohoku University entrance exam 1966

August 10, 2006
calculusintegrationtrigonometrycalculus computations

Problem Statement

Find the value of aa for which ∫0π2∣asin⁡x−cos⁡x∣ dx (a>0)\int_{0}^{\frac{\pi}{2}}|a\sin x-\cos x|\ dx\ (a>0) is minimized.
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