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WZ
Numerade Educator

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Problem 46 Hard Difficulty

Sketch the region and find its area (if the area is finite).

$ S = \{ (x, y) \mid -2 < x \le 0, 0 \le y \le \frac{1}{\sqrt{x + 2}} $

Answer

Area $=2 \sqrt{2}$

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Video Transcript

the problem is sketched and region and find his area. Look at the graph. The region is Shadid here. We need to find the area of this part we can use Integral from next to two zero was a function one over routine exposed to Dean to be not the area of this region. This is an improper, integral a definition. This is the cultures that limit he goes to next year too. Empty girl from tea to zero of the function One over Return Express to Yes. So we've computed a happening The integral first Look at this definite integral. This's kowtow one over on half Juan X class two, two, one of us wass and start, this is negative. One half is ineffective Have plus one from she too. Cyril Simula varieties functions so this is one over half. So this is two Herms X plus to Joe, one half from he to zero on the plugging zero auntie to dysfunction. This's two hams. Two, you are half on minus two hams. He passed too on half power. Now when he goes to negative too, she plus two goes to zero. So this function goes to two. Tough. So when he goes to met, you too says area of this region is two times routes off too.