The area of the smaller segment cut off from the circle $x^2 + y^2 = 9$ by the line $x = 1$ is

The area of the region bounded by the curve $y=\sqrt{49-x^2}$ and the $X$-axis is

Area of the region bounded by the curve $y=x|x|$,$X$-axis and lines $x=0$ and $x=1$ is . . . . . . sq. units.

The area (in sq units) between the curve $y^2 = 8x$ and its latus rectum is

If the line $x=\alpha$ divides the area of region $R=\{(x, y) \in \mathbb{R}^2: x^3 \leq y \leq x, 0 \leq x \leq 1\}$ into two equal parts,then which of the following is true?
$[A] \ 0 < \alpha \leq \frac{1}{2}$
$[B] \ \frac{1}{2} < \alpha < 1$
$[C] \ 2 \alpha^4 - 4 \alpha^2 + 1 = 0$
$[D] \ \alpha^4 + 4 \alpha^2 - 1 = 0$

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: