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# Determine whether each integral is convergent or divergent. Evaluate those that are convergent.$\displaystyle \int_0^\infty e^{-\sqrt{y}}\ dy$

## 2, Convergent

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

the problem is determined by the Agent Negro is converted or a verdant while you're at it. So's that convergent This improper, integral definition. This is equal to the limit. He goes to infinity and the integral is from zero to t eat connective root of wine You want we compute the definite integral first But this Stephanie grow we can use youself contusion first, let you issue go too Negative return. Why a new squire if you go to why to you? Do you Is he going to? Do you know why? Now this staff meeting Integral If we go too zero to next t This is each of you hams. Who are you? You here we use the my third off the integration by parts This is equal to into girl from zero to negative return Active relative t And this is to you. You This's Yuko too to you You you drama Zero connective rooted He minus into a girl zero to ninety root of off the function to have eat you You This is you go to no native root of Qi two Make it two towns route off to inter Native T minus zero Myers and I had to write him with. This function is to rams into you from dear old negative fruit of tea. Yeah, this is Echo Two negative. Two times dutiful tea into negative narrative. He minus to house into connective minus two. When he goes to infinity, this part goes to zero on this part also goes to zero. The answer is ICO too. Two. Is this improper? Integral is commitment, and the value is

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#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp