?Sketch the region and find its area (if the area is finite).\(S=\left\{(x, \ y) \mid x

Chapter 7, Problem 49

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QUESTION:

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

\(S=\left\{(x, \ y) \mid x \geqslant 1, \ 0 \leqslant y \leqslant e^{-x}\right\}\)

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QUESTION:

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

\(S=\left\{(x, \ y) \mid x \geqslant 1, \ 0 \leqslant y \leqslant e^{-x}\right\}\)

ANSWER:

Step 1 of 3

We are given that

Area below the curve  and above -axis in the interval  is given by

Note that  must be

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