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WZ

# Sketch the region and find its area (if the area is finite).$S = \{ (x, y) \mid x \ge 1, 0 \le y \le e^{-x} \}$

## $\lim _{t \rightarrow \infty}\left(-e^{-t}+e^{-1}\right)=0+e^{-1}=1 / e$

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

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### Video Transcript

the problem is sketch the region and find its area. Look at this graph. We need to find his carrier off this part Here we can use the integral from want to infinity. I was a function into negative ass. Yes, to the note area. With this part This's an improper, integral A definition. This's equal to Lim a goes to infinity into grow from one, eh into making backs? Yes, this's a limit and he goes to infinity and on high derivative of each negative mass is equal to negative into negative axe from one toe, eh is in cultures that limit it goes to energy Negative. You to make two of a minus in tow make to want the one a goes to infinity in to make the way Those two there are is part of it goes to zero The answer is because you into makes you want Sir, the area is ICO Tow it to make you one

WZ

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp