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Published in:
2003 | OriginalPaper | Chapter
Anwendungen
Author : Harro Heuser
Published in: Lehrbuch der Analysis
Publisher: Vieweg+Teubner Verlag
Included in: Professional Book Archive
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Da für alle x ∈ [0, π/2] stets 0 ⩽ sin x ⩽ 1 ist, gilt für diese x und für alle k ∈ N die Ungleichung sin2k+1x ⩽ sin2kx ⩽ sin2k-1x. Aus ihr folgt durch Integration 94.1$$\int\limits_0^{\pi /2} {{{\sin }^{2k + 1}}xdx\underline < \int\limits_0^{\pi /2} {{{\sin }^{2k}}} xdx\underline < \int\limits_0^{\pi /2} {{{\sin }^{2k - 1}}} xdx} $$.