The area of the region bounded by the curve $y=\sin x$ between $x=-\pi$ and $x=\frac{3\pi}{2}$ is

The area of the smaller part between the circle $x^2 + y^2 = 4$ and the line $x = 1$ is

The area between the curve $y = \sin^2 x$,the $x$-axis,and the ordinates $x = 0$ and $x = \frac{\pi}{2}$ is:

Area enclosed by the curve $y = f(x)$ that is defined parametrically as $x = \frac{1 - t^2}{1 + t^2}, y = \frac{2t}{1 + t^2}$ (where $t \in R$) is equal to

$A$ quadratic polynomial $y = f(x)$ with absolute term $3$ neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$. The coefficient of the leading term of the polynomial is unity. $A$ point $A(x_1, y_1)$ with abscissa $x_1 = 1$ and a point $B(x_2, y_2)$ with ordinate $y_2 = 11$ are given in a Cartesian rectangular system of coordinates $OXY$ in the first quadrant on the curve $y = f(x)$,where $O$ is the origin. The area bounded by the curve $y = f(x)$ and the line $y = 3$ is: (in $/3$)

Find the area of the region $\{(x, y): 0 \leq y \leq x^{2}+1, 0 \leq y \leq x+1, 0 \leq x \leq 2\}$.