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

## Area $=1$

#### Topics

Integration Techniques

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### Video Transcript

the problem is sketch the region and find its area. Look at this graph we need to find It's the roof area off. It's a shady depart this part we can use and grow from the road to sanity of it X temps in connected last e x to denounce area on this part. But this improper, integral. But that mission, this is equal to the limit. It goes to infinity into go from zero to a ex Thames into make two blacks. Yes, we computed this definite integral first for this death it into zero. We used my third off integration, My parse. This is equal chewed into girl from there to a thanks. The conectiv in tow make you x use the my third wind charisma. Pars, this is Echo two ex rams. Negative, you two. Next, Lex. From zero to a minus into door from zero to a negative to make you X. Yes, thiss is a culture plugging a zero to this function. Is that control connective? A ham too, Next to fade minus zero. Minus the class. My last month in the class into your off into Mickey Lax from there to a Zico connective eh into negative, eh? Maya's Tio? Maybe to us from zero. Since this is Echo Two negative, eh? Into the night away minus into negative, eh? Minus into make two zero minus one. There's someone I want a goes toe infinity! It's what it goes to zero. This part also goes to D'Oh. What's this one? You can use the limit. It goes to zero. This negative a over into a Now it goes toe infinity and then use a bean Has rules. This is culture. Damn It makes you want over you too, eh? It goes to infinity. This is gusto. Here. His answer is is zero minus Make to want. So this is you. Go to one. His area of this region is equal to one.

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#### Topics

Integration Techniques

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