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WZ
Numerade Educator

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Problem 50 Medium Difficulty

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

$ \displaystyle \int_1^\infty \frac{1 + \sin^2 x}{\sqrt{x}}\ dx $

Answer

Divergent.

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Video Transcript

problem is used that he comparison theory, um, to determine why this integral discordant or there wouldn't. First, we have the following result and to grow from one to infinity off of the function one over ice to peace Power Jax on What's this integral? This integral is convergent If he is greedy is online on the divergent If is smaller than one now So our integral off this function Now just listen to girl from one to infinity one plus sign I squire over motive ax the ax This scientific square is created and zero so dysfunction always bigger is one over you tell blacks this's really on the fourth dysfunction. The cat is a result here this is ax to one half He is They go to one half, Then we're half is small One is this function that word didn't Now our function is greeted and dysfunction. Our function is how so That wouldn't buy the cereal off comparison cereal