Area Under Curves

The area of the region included between the curves $x^{2}+y^{2}=a^{2}$ and $\sqrt{\left|x\right|}+\sqrt{\left|y\right|}=\sqrt{a}\left(a>0\right)$ is

The point $([P+1], [P])$ (where, $[x]$ is the greatest integer function) lying inside the region bounded by the circle ${x}^{2}+{y}^{2}-2x-15=0$ and ${x}^{2}+{y}^{2}-2x-7=0$, then

The area under the curve $y=|\cosx-\sinx|, 0≤x≤\frac{π}{2}$ and above $X$-axis, is

A wire $34 \mathrm{~cm}$ long is to be bent in the form of a quadrilateral of which each angle is $90^{\circ} .$ What is the maximum area which can be enclosed inside the quadrilateral?

The area bounded by the $x$ -axis, the curve $y=f(x)$ and the lines $\mathrm{x}=1, \mathrm{x}=\mathrm{b},$ is equal to $\sqrt{\mathrm{b}^{2}+1}-\sqrt{2}$ for all $b>1,$ then $f(x)$ is

The area bounded by the curve $y=\sin x, x$ -axis and the ordinates $x=0$ and $x=\pi / 2$ is

What is the area bounded by \(y=\tan x, y=0\) and \(x=\frac{\pi}{4} ?\)

If \(\mathrm{I}_{\mathrm{m}}=\int_1^{\mathrm{e}}(\ln \mathrm{x})^{\mathrm{m}} \mathrm{dx}\), where \(\mathrm{m} \in \mathrm{N}\), then \(I_{10}+10 I_9\) is equal to -

The area enclosed by the curves $y=x^3$ and $y=\sqrt{x}$ is

If $a, c, b$ are in GP, then the area of the triangle formed by the lines $a x+b y+c=0$ with the coordinates axes is equal to

The line $y=m x$ bisects the area unclosed by lines $x=0, y=0$ and $x=\frac{3}{2}$ and the curve $y=1+4 x-x^2$. Then, the value of $m$ is

The area of the region bounded by the curves $x$ $=y^2-2$ and $x=y$ is