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Today's calculation of Integral 747

Source: 2011 Kanazawa University entrance exam

August 29, 2011
calculusintegrationtrigonometryinequalitiescalculus computations

Problem Statement

Prove that ∫04(1−cos⁡x2)exdx≤−2e2+30.\int_0^4 \left(1-\cos \frac{x}{2}\right)e^{\sqrt{x}}dx\leq -2e^2+30.
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