Question

The area of the bounded by the curve xy = c, x-axis and between the lines x = 1 and x = 4, is ____________.

Answer 1

To find: area of the region bounded by the curve xy = c, x-axis and between the lines x = 1 and x = 4

The required area of the region = ${\int }_1^{4}ydx$
Thus,
$$\begin{gathered} \mathrm{Required}\mathrm{area}={\int }_1^{4}ydx \\ ={\int }_1^4\left(\frac{c}{x}\right)dx \\ =c{\left(\log x\right)}_1^4 \\ =c\left(\log 4-\log 1\right) \\ =c\left(\log 2^2-0\right) \\ =c\left(2\log 2\right) \\ =2c\log 2 \\ \mathrm{Thus},\mathrm{Area}=2c\log 2\mathrm{sq}.\mathrm{units} \end{gathered}$$


Hence, the area of the region bounded by the curve xy = c, x-axis and between the lines x = 1 and x = 4, is $\underline{2c\log 2\mathrm{sq}.\mathrm{units}}.$