Question
The area of the region enclosed by the curves $$y = x,\,x = e,\,y = \frac{1}{x}$$ and the positive $$x$$-axis is
A.
$$1$$ square unit
B.
$$\frac{3}{2}$$ square unit
C.
$$\frac{5}{2}$$ square unit
D.
$$\frac{1}{2}$$ square unit
Answer :
$$\frac{3}{2}$$ square unit
Solution :
Area of required region $$AOBC :$$
$$\eqalign{ & = \int\limits_0^1 {x\,dx} + \int\limits_1^e {\frac{1}{x}dx} \cr & = \frac{1}{2} + 1 \cr & = \frac{3}{2}\,\,{\text{sq}}{\text{. units}} \cr} $$
Area of required region $$AOBC :$$
$$\eqalign{ & = \int\limits_0^1 {x\,dx} + \int\limits_1^e {\frac{1}{x}dx} \cr & = \frac{1}{2} + 1 \cr & = \frac{3}{2}\,\,{\text{sq}}{\text{. units}} \cr} $$