Using integration,find the area of the region bounded by the triangle whose vertices are $(-1, 0)$,$(1, 3)$,and $(3, 2)$.

Area bounded by the curves $y = |x| - 1$ and $y = -|x| + 1$ is (in square units)

Find the area bounded by the curve $y = x{e^{{x^2}}}$,the $x$-axis,and the ordinates $x = 0$ and $x = a$.

Find the area of the region bounded by the curve $y=x^{2}$ and the line $y=4$. (in $/3$)

$A$ 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:

Using the method of integration,find the area bounded by the curve $|x|+|y|=1$.