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Numerade Educator

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Problem 51 Medium Difficulty

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

$ \displaystyle \int_1^\infty \frac{x + 1}{\sqrt{x^4 - x}}\ dx $

Answer

Diverges

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Video Transcript

Hello. Welcome to this lesson. In this lesson, we'll use that comparison test to show whether the whole of the integral converges or diverges. So what, we'll compare it against this. So we have one over skirt of X four minus X, and this is always greater than one over X okay, or better than or equal to. But we know that the script of, uh, the integral from one to infinity of one of our x dx mhm that is equal to land X from one to infinity. That is a call to infinity minus one diver. Jeez. So if if this diverges, then the whole of this X plus one cool. So the idea here is that if gee of eggs 15 years Jean of X is less than f of X and then of X diabetes, Ben F of X will diverge, given the same the same bounce. Okay, sometimes your time. This is the end of the lesson.