JEE MAIN - Mathematics (2011 - No. 11)
The area of the region enclosed by the curves $$y = x,x = e,y = {1 \over x}$$ and the positive $$x$$-axis is :
$$1$$ square unit
$${3 \over 2}$$ square units
$${5 \over 2}$$ square units
$${1 \over 2}$$ square unit
Explication
Area of required region $$AOCB$$
$$ = \int\limits_0^1 {xdx} + \int\limits_1^e {{1 \over x}dx = {1 \over 2}} + 1 = {3 \over 2}$$ sq. units
$$ = \int\limits_0^1 {xdx} + \int\limits_1^e {{1 \over x}dx = {1 \over 2}} + 1 = {3 \over 2}$$ sq. units