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WZ
Numerade Educator

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Problem 54 Medium Difficulty

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

$ \displaystyle \int_0^\pi \frac{\sin^2 x}{\sqrt{x}}\ dx $

Answer

$\int_{0}^{\pi} \frac{\sin ^{2} x}{\sqrt{x}} d x$ is convergent

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Video Transcript

the problem is, use a comparison theory, um, to determine whether the integral is converted or that burden here we will use one result this integral from you're from zero to pi. One hour acts to his power. So here you can replace pie to any number eight Any council number eight This is the verdant if he is greater than one and the calmer didn't yes is smaller than what Now our function is sine x square over route of blacks This integral from zero to pi dysfunction Sign square over root of facts Jacks Since signing a square is always smaller than one, this function is smaller than one over acts to one half smile with the ex. No, look at here. So one half is smaller than one. Mhm. This integral is convergent by comparison. Their realm the integral from zero to pi over the function syntax square root of wax is also convergent