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Question-54073




Question Number 54073 by cesar.marval.larez@gmail.com last updated on 28/Jan/19
Answered by estudiante last updated on 28/Jan/19
Vemos q es una integral impropia de tipo I:  lim_(R→∞)  ∫_a ^R x^n dx = lim_(R→∞)  ∣(x^(n+1) /(n+1))∣_a ^R = lim_(R→∞)  ((R^(n+1) /(n+1)) −(a^(n+1) /(n+1)))= ∞  La integral por lo tanto diverge a +∞
$${Vemos}\:{q}\:{es}\:{una}\:{integral}\:{impropia}\:{de}\:{tipo}\:{I}: \\ $$$$\underset{{R}\rightarrow\infty} {\mathrm{lim}}\:\int_{{a}} ^{{R}} {x}^{{n}} {dx}\:=\:\underset{{R}\rightarrow\infty} {\mathrm{lim}}\:\mid\frac{{x}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\mid_{{a}} ^{{R}} =\:\underset{{R}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{R}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\:−\frac{{a}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\right)=\:\infty \\ $$$${La}\:{integral}\:{por}\:{lo}\:{tanto}\:{diverge}\:{a}\:+\infty \\ $$

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