Area Under the Curves

The area of the region enclosed between the parabolas y² = 2x $$-$$ 1 and y² = 4x $$-$$ 3 is

The area bounded by the curves $$y=|x-1|+|x-2|$$ and $$y=3$$ is equal to :

The area bounded by the curves $$y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|$$ and $$y = \left| {\ln \left| x \right|} \right|$$ is :

The area of the region bounded by the curves $$y = \left| {x - 1} \right|$$ and $$y = 3 - \left| x \right|$$ is :

The area of the region bounded by the curves $$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :

The parabolas $${y^2} = 4x$$ and $${x^2} = 4y$$ divide the square region bounded by the lines $$x=4,$$ $$y=4$$ and the coordinate axes. If $${S_1},{S_2},{S_3}$$ are respectively the areas of these parts numbered from top to bottom ; then $${S_1},{S_2},{S_3}$$ is :

The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ is :

The area of the plane region bounded by the curves $$x + 2{y^2} = 0$$ and $$\,x + 3{y^2} = 1$$ is equal to :

The area of the region bounded by the parabola $${\left( {y - 2} \right)^2} = x - 1,$$ the tangent of the parabola at the point $$(2, 3)$$ and the $$x$$-axis is :

The area bounded by the curves $$y = \cos x$$ and $$y = \sin x$$ between the ordinates $$x=0$$ and $$x = {{3\pi } \over 2}$$ is

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

The area between the parabolas $${x^2} = {y \over 4}$$ and $${x^2} = 9y$$ and the straight line $$y=2$$ is :

The area (in square units) bounded by the curves $$y = \sqrt {x,}$$ $$2y - x + 3 = 0,$$ $$x$$-axis, and lying in the first quadrant is :

The area of the region described by $$A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} \le 1} \right.$$ and $$\left. {{y^2} \le 1 - x} \right\}$$ is :

The area (in sq. units) of the region described by $$\left\{ {\left( {x,y} \right):{y^2} \le 2x} \right.$$ and $$\left. {y \ge 4x - 1} \right\}$$ is :

The area (in sq. units) of the region described by A= {(x, y) $$\left| {} \right.$$y$$\ge$$ x² $$-$$ 5x + 4, x + y $$\ge$$ 1, y $$\le$$ 0} is :

The area (in sq. units) of the region $$\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}$$ is :

If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is -

The area (in sq. units) of the smaller portion enclosed between the curves, x² + y² = 4 and y² = 3x, is :