How could you tell that the improper integral from 0 to infinity of: e^(-x)*sqrt(1+e^(-2x)) dx converges WITHOUT actually computing it? It is obvious from the graph, but how can you argue this otherwise?
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Originally Posted by zhupolongjoe How could you tell that the improper integral from 0 to infinity of: e^(-x)*sqrt(1+e^(-2x)) dx converges WITHOUT actually computing it? It is obvious from the graph, but how can you argue this otherwise? Consider
Ah yes, and clearly the larger integral converges, and so alas! Thanks
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