If the area above x-axis, bounded by the curves $y = 3^{\beta x}$, $x = 0$ and $x = 3$ is $\frac{26}{\log_e 3}$, then the value of $\beta$ is:

The area (in sq. units) of the region bounded by the curve $y = 2x^3$, $x$ - axis and ordinates $x = -1$ and $x = 1$ is:

The area (in sq. units) bounded between the curves $x=e^y$, $x=e$ and x-axis in the first quadrant is

The supply function for a commodity is $p = x^2 + x + 3$. The producer's surplus when $x = 3$ is,

Area of the region bounded by $y = x^2$ and the line $y = 16$ is

The area bounded by the curve $|-x|+|-y|=2$ is

The area enclosed between the curves $y = x^2$ and $x = y^2$ is