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WZ
Numerade Educator

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Problem 5 Easy Difficulty

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_3^\infty \frac{1}{(x - 2)^{\frac{3}{2}}}\ dx $

Answer

2, Convergent

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Video Transcript

so the problem is determined. Why does this Indigo Royals component that Wouldn't. This is an improper, integral my definition. This's Iko too. That limit off he goes to infinity into girl off dysfunction One over X minus two. Yeah. Three over to power from three tea, Jax. And then this is a coach is a limit. He goes to infinity and we need to integrate dysfunction that this is a con too negative. Two times X minus two makes you want half around the rain too. This this culture is a limit. He goes to infinity. So we need to plug in Teo three years. So this is next you two hams minus two, two, ninety one, half minus one. And we know when he goes to infinity. He minus two to ninety one. Half power zero. This is that you got to next. You two halves next you want to. This is two. So this integral is commitment. Ondas value is two