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Question Number 147539 by alcohol last updated on 21/Jul/21

s h o w t h a t

\frac{1}{2} \int_{1}^{2} \frac{1}{x^{5}} d x ⩽ \int_{1}^{2} \frac{1}{x^{4} + 1} d x ⩽ \int_{1}^{2} \frac{1}{x^{4}}

Answered by puissant last updated on 21/Jul/21

\forall x \in [1; 2],

x^{4} ⩽ x^{4} + 1 ⩽ {2 x}^{5} \Rightarrow \frac{1}{{2 x}^{5}} ⩽ \frac{1}{x^{4} + 1} ⩽ \frac{1}{x^{4}}

\Rightarrow \frac{1}{2} \int_{1}^{2} \frac{1}{x^{5}} dx ⩽ \int_{1}^{2} \frac{1}{x^{4} + 1} ⩽ \int_{1}^{2} \frac{1}{x^{4}} . .

Answered by puissant last updated on 21/Jul/21

polytech yaound \overset{´}{e} premi \overset{`}{e r e} \overset{´}{e p r e u v e} . .

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