Recall the following property of integrals: If (t) g(t) for all t 0, then for

Recall the following property of integrals: If ƒ(t) ≥ g(t) for all t ≥ 0, then for all x ≥ 0,

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f* f(1)dt = f*g(1) dt z The inequality et ≥ 1 holds for t≥ 0 because e > 1. Use (4) to prove that e 21+x for x ≥ 0 Then prove, by successive integration, the following inequalities (for x ≥ 0): 1 @³21+x+ 2 x² 91 1 e²21+x+ x² + ² 2