Using the method of integration,find the area of the triangle $ABC$,whose vertices are $A(2,0)$,$B(4,5)$,and $C(6,3)$.

The area bounded by the curve $y = x^3$,the $x$-axis,and the two ordinates $x = 1$ and $x = 2$ is equal to:

$A$ farmer $F_1$ has a land in the shape of a triangle with vertices at $P(0,0)$,$Q(1,1)$,and $R(2,0)$. From this land,a neighbouring farmer $F_2$ takes away the region which lies between the side $PQ$ and a curve of the form $y = x^n$ $(n > 1)$. If the area of the region taken away by the farmer $F_2$ is exactly $30\%$ of the area of $\triangle PQR$,then the value of $n$ is:

The area of the region bounded by the curve $y = x^3$ and the lines $y = 8$ and $x = 0$ is ... square units.

Area of the region bounded by $y=|x|$ and $y=-|x|+2$ is

The area enclosed (in square units) by the curve $y=x^4-x^2$, the $x$-axis and the vertical lines passing through the two minimum points of the curve is