The area of the region bounded by the lines $y=mx$,$x=1$,$x=2$,and the $x$-axis is $6$ sq. units. Then,the value of $m$ is:

The area of the region bounded by the parabola $y^{2}=8x$ and its latus rectum is

If $\int\limits_0^1 {(4x^3 - f(x))f(x)dx = \frac{4}{7}}$,then the area of the region bounded by $y = f(x)$,the $x$-axis,and the ordinates $x = 1$ and $x = 2$ is:

Let $f: R \rightarrow R$ be a twice differentiable function such that $f(x + y) = f(x) f(y)$ for all $x, y \in R$. If $f^{\prime}(0) = 4a$ and $f$ satisfies $f^{\prime \prime}(x) - 3a f^{\prime}(x) - f(x) = 0$,$a > 0$,then the area of the region $R = \{(x, y) \mid 0 \leq y \leq f(ax), 0 \leq x \leq 2\}$ is:

Find the area of the region bounded by the line $y=3x+2$,the $x$-axis,and the ordinates $x=-1$ and $x=1$.

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