## Task Condition

Calculate the area of the figure bounded by the graphs of the functions:

$$
y=\frac{e^{1 / x}}{x^{2}}, y=0, x=2, x=1
$$
## Solution

Integrals 14-26

![](https://cdn.mathpix.com/cropped/2024_05_22_aa6951b1e92815ea34b6g-49.jpg?height=1419&width=1428&top_left_y=1095&top_left_x=448)

The desired area \( S \) is:

\[
S=\int_{1}^{2} \frac{e^{1 / x}}{x^{2}} d x=-\left.e^{1 / x}\right|_{1} ^{2}=-e^{1 / 2}+e^{1}=e-\sqrt{e}
\]

Source — «http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\� \%D0\%9A\%D1\%83\%D0\%B7\%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B}+14-26 \%$

Categories: Kuznetsov Problem Book Integrals Problem 14 | Integrals

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## Problem Kuznetsov Integrals 14-27

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