The area (in sq. units) of the region enclosed by $\{(x, y) \mid y \leq x^2, xy \leq 8, y \geq 1\}$ is...

If the area bounded by $y = x^3 + ax$ (where $a > 0$), the $x$-axis and the lines $x = -2$ and $x = 1$ is $\dfrac{37}{4}$ square units, then $\ldots$

The area (in square units) bounded by the line $y = x$, the X-axis and the lines $x = -2$ and $x = 4$ is...

The area of the region bounded by curves $y = \sin x, y = \cos x$ and the lines $x = 0$, $x = \dfrac{\pi}{4}$ is