If the area enclosed between the curves $y = kx^2$ and $x = ky^2$ $(k > 0)$ is $1$ square unit,then $k$ is

Let $T$ be the tangent to the ellipse $E: x^{2}+4 y^{2}=5$ at the point $P(1,1)$. If the area of the region bounded by the tangent $T$,ellipse $E$,lines $x=1$ and $x=\sqrt{5}$ is $\alpha \sqrt{5}+\beta+\gamma \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)$,then $|\alpha+\beta+\gamma|$ is equal to $....$

If the area of the larger portion bounded between the curves $x^2+y^2=25$ and $y=|x-1|$ is $\frac{1}{4}(b \pi+c)$,where $b, c \in N$,then $b+c$ is equal to $ . . .. .. $

The area (in sq. units) enclosed by the curves $y=2x-x^2$ and $y=x^2-2x-6$ is

The area (in square units) bounded by the curves $y^2=4x$ and $x^2=4y$ in the plane is

Area of the region bounded by the curves $y = \sin x$ and $y = x$ between the lines $x = 0$ and $x = 2\pi$ is: