The area of the region enclosed by the curves $y=x, x=e, y=\frac{1}{x}$ and the positive $x$-axis is

The area of the region enclosed by the curves $y=x, x=e, y=\frac{1}{x}$ and the positive $x$-axis is
  1. 1 square units
  2. $\frac{3}{2}$ square units
  3. $\frac{5}{2}$ square units
  4. $\frac{1}{2}$ square units

Solution


Area $=\int_0^1 x d x+\int_1^e \frac{1}{x} d x=\frac{1}{2}+1=\frac{3}{2}$

Asked in: JEE Main 2011

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