Find the area bounded by the curves $x = \sqrt{y - 1}$ and $y = x + 1$.

In the figure given below,if the areas of the two regions are equal,then which of the following is true?

The area (in square units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=3$,is

If the area of the region bounded by the curves $y^2-2y=-x$ and $x+y=0$ is $A$,then $8A$ is equal to

Let the area of the region $\{(x, y): x-2y+4 \geq 0, x+2y^2 \geq 0, x+4y^2 \leq 8, y \geq 0\}$ be $\frac{m}{n}$,where $m$ and $n$ are coprime numbers. Then $m+n$ is equal to

The area (in sq. units) of the region given by $R = \{(x, y) : \frac{y^2}{2} \leq x \leq y + 4\}$ is