The area bounded by the curve $y=|x-2|$,$x=1$,$x=3$ and $X$-axis is

Area of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is

If the line $y=mx$ bisects the area enclosed by the lines $x=0, y=0, x=\frac{3}{2}$ and the curve $y=1+4x-x^2$,then $12m$ is equal to ..... .

The area bounded by the $x-$ axis,the curve $y = f(x)$ and the lines $x = 1$ and $x = b$ is equal to $\sqrt{b^2 + 1} - \sqrt{2}$ for all $b > 1$. Then $f(x)$ is:

The graphs of $f(x) = x^2$ and $g(x) = cx^3$ (where $c > 0$) intersect at the points $(0, 0)$ and $\left( \frac{1}{c}, \frac{1}{c^2} \right)$. If the area of the region lying between these graphs over the interval $[0, 1/c]$ is equal to $2/3$,then the value of $c$ is:

The area bounded by the curve $y=x^3-3x^2+2x$ and the $X$-axis is (in square units)