Area Under the Curves

The area of the region enclosed by the parabolas $y=4 x-x^2$ and $3 y=(x-4)^2$ is equal to :

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

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 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 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 of the region $\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\}$ 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 :

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