The area of the region bounded by the curve $y=|x-5|$,the $X$-axis,and the lines $x=5$ and $x=6$ is . . . . . . sq. units.

The area bounded by the curves $y = -\sqrt{-x}$ and $x = -\sqrt{-y}$ where $x, y \le 0$ is:

The area between the curve $y = \cos x$ and the $x$-axis for $0 \le x \le 2\pi$ is:

The area (in square units) lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is

In the figure,$AOBA$ is the part of the ellipse $9x^{2} + y^{2} = 36$ in the first quadrant such that $OA = 2$ and $OB = 6$. Find the area between the arc $AB$ and the chord $AB$.

Prove that the curves $y^{2}=4x$ and $x^{2}=4y$ divide the area of the square bounded by $x=0, x=4, y=4$ and $y=0$ into three equal parts.