IMC 2010 · Problem 1

Day 117th IMC · Blagoevgrad, Bulgaria

Statement

Let 0<a<b0 < a < b. Prove that

ab(x2+1)ex2dxea2eb2.\int_a^b (x^2 + 1)e^{-x^2}\,dx \ge e^{-a^2} - e^{-b^2}.

Official solution

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