The area of the region bounded by the parabola $y=x^{2}-4x+5$ and the straight line $y=x+1$ is

The area bounded by the parabolas $y = 9x^2$, $y = \frac{x^2}{16}$ and the line $y = 1$ is

The area of the shorter region bounded by $|y| = 4 - x^2$ and $|y| = 3x$ is given by $\left( 3K + \frac{1}{3} \right)$ sq-unit,where $K$ is equal to:

The area enclosed by the curves $y = x^2$,$y = x^3$,$x = 0$,and $x = p$,where $p > 1$,is $1/6$. The value of $p$ is:

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 straight lines $x = 0, x = 2$ and the curves $y = 2^x, y = 2x - x^2$ is