The area of the region common to the parabolas $4y^2 = 9x$ and $3x^2 = 16y$ is...

The area (in sq. units) in the first quadrant bounded by the parabola $y = x^2 + 1$,the tangent to it at the point $(2, 5)$,and the coordinate axes is

The area (in square units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=3$,is

Let the area of the region bounded by the curve $y=\max\{\sin x, \cos x\}$, lines $x=0, x=\frac{3\pi}{2}$ and the x-axis be $A$. Then, $A+A^{2}$ is equal to:

Let $A_{1}$ be the area of the region bounded by the curves $y = \sin x$,$y = \cos x$ and the $y$-axis in the first quadrant. Also,let $A_{2}$ be the area of the region bounded by the curves $y = \sin x$,$y = \cos x$,the $x$-axis and $x = \frac{\pi}{2}$ in the first quadrant. Then ..... .

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