The area bounded by the parabola $y^2=x$,the straight line $y=4$ and the $Y$-axis is

The values of a function $f(x)$ at different values of $x$ are as follows:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$f(x)$	$2$	$3$	$6$	$11$	$18$	$27$

Then,the approximate area (in square units) bounded by the curve $y=f(x)$ and the $x$-axis between $x=0$ and $x=5$,using the Trapezoidal rule,is:

The area bounded by the curve $y = x^3$,the $x$-axis,and the two ordinates $x = 1$ and $x = 2$ is equal to:

Find the area of the region in the first quadrant enclosed by the $x-$ axis,the line $x=\sqrt{3} y$ and the circle $x^{2}+y^{2}=4$.

Find the area of the region in the first quadrant enclosed by the $x-$ axis,the line $y=x,$ and the circle $x^{2}+y^{2}=32$. (in $\pi$)

The area (in sq. units) of the smaller part of the circle $x^2+y^2=a^2$ cut off by the line $x=\frac{a}{\sqrt{2}}$ is