The area of the region bounded by the curve $y=x$,the lines $x=1$ and $x=10$ using integration is . . . . . . sq. units.

The area enclosed by $y=3x-5$, $y=0$, $x=3$, and $x=5$ is

If $y = 2 \sin x + \sin 2x$ for $0 \le x \le 2 \pi ,$ then the area enclosed by the curve and the $x-$axis is

The area of the smaller region bounded by the circle $x^2 + y^2 = 4$ and the line $x = 1$ 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 of the region bounded by the curve $y=2x-x^2$ and the $x$-axis is