If the area of the region $\{(x, y): 1+x^2 \leq y \leq \min \{x+7, 11-3x\}\}$ is $A$,then $3A$ is equal to

The area (in sq. units) of the region bounded by the lines $x=0, x=\frac{\pi}{2}$ and $f(x)=\sin x, g(x)=\cos x$ is

The area of the region lying above the $X$-axis and included between the circle $x^{2}+y^{2}=2ax$ and the parabola $y^{2}=ax$, $a>0$ is

If the area of the region enclosed by the curve $ay = x^2$ and the line $x + y = 2a$ is $ka^2$, then $k =$

$OABC$ is a unit square where $O$ is the origin and $B=(1,1)$. The curves $y^2=x$ and $x^2=y$ divide the area of the square into three parts $a_1, a_2, a_3$. If $a_1, a_2, a_3$ are the areas (in sq units) of these parts respectively,then $a_1+2a_2+3a_3=$

The area bounded by the curves $y = (x + 1)^2$,$y = (x - 1)^2$ and the line $y = \frac{1}{4}$ is