Area of the region enclosed between the curves $y^2=4(x+7)$ and $y^2=5(2-x)$ is

The area of the region bounded by the line $y=x$ and the curve $y=x^3$ is

If $f(x)$ is a continuous,increasing,and odd function such that $\int_{-1}^{4} f(x) \,dx = 10$ and $\int_{0}^{1} f(x) \,dx = \frac{3}{2}$,then the area bounded by $y = f(x)$,the $x$-axis,and the ordinates $x = -4$ and $x = 4$ is:

Let the line $x=-1$ divide the area of the region $\{(x,y):1+x^{2}\le y\le3-x\}$ in the ratio $m:n$, where $\gcd(m,n)=1$. Then $m+n$ is equal to

Area of the region (in square units) enclosed by the curves $y^2=8(x+2)$,$y^2=4(1-x)$ and the $Y$-axis is

The area bounded by the curve $y = e^x$ and the lines $y = |x - 1|, x = 0, x = 2$ is given by