Solution assignment 02 Area and volume

Assignment 2

Calculate the area which is enclosed by $y=\displaystyle\frac{1}{x}$ , the lines $x=1$ , $x=3$ and $y=2$ .

Solution

The area can be calculated as follows: calculate the area of the rectangle through the points $(\displaystyle\frac{1}{2},2)$ and $(3,0)$ and subtract the area of the area enclosed by the lines $x=\displaystyle\frac{1}{2}$ and $x=3$ , the $X$ -axis and the graph of $y=\displaystyle\frac{1}{x}$ . This yields the following formula:

$\displaystyle2\frac{1}{2}\cdot2-\int_{\frac{1}{2}}^3\frac{1}{x}dx=$

$=5-[\ln(x)]_\frac{1}{2}^3=5-(\ln(3)-\ln(\frac{1}{2}))=5-\ln(3)-\ln(2)$

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Solution assignment 02 Area and volume

Assignment 2

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