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

If $A$ is the area in the first quadrant enclosed by the curve $C: 2x^2 - y + 1 = 0$,the tangent to $C$ at the point $(1, 3)$ and the line $x + y = 1$,then the value of $60A$ is

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

If the area (in sq. units) bounded by the parabola $y^2 = 4\lambda x$ and the line $y = \lambda x$,$\lambda > 0$,is $\frac{1}{9}$,then $\lambda$ is equal to

The area bounded by the curves $y = (x + 1)^2$,$y = (x - 1)^2$ and the line $y = 0$ is

If $f(x)$ is a continuous,increasing,and odd function such that $\int_{-1}^{4} f(x) \,dx = 10$ and $\int_{0}^{1} f(x) \,dx = \frac{3}{2}$,then the area bounded by $y = f(x)$,the $x$-axis,and the ordinates $x = -4$ and $x = 4$ is: