The area bounded by the curve $y = 4x - x^2$ and the $X$-axis in square units is:

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

If the area bounded by the curve $y = x^3 + ax$ (where $a > 0$), the $x$-axis, and the lines $x = -2$ and $x = 1$ is $\frac{37}{4}$ square units, find the value of $a$.

Let $y = g(x)$ be the inverse of a bijective mapping $f : R \rightarrow R$ defined by $f(x) = 3x^3 + 2x$. The area bounded by the graph of $g(x)$,the $x-$axis,and the ordinate at $x = 5$ is:

If the area bounded by the curve $x^2=4y$,the $X$-axis,and the line $x=4$ is divided into two equal areas by the line $x=\alpha$,then the value of $\alpha$ is ...

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